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The ratio of the present age of the two brothers is 11 : 13 and 6 years ago the ratio of their ages was 4 : 5. What will be the ratio of their ages after 5 years?
If the ratio of the ages of A and B is 3 : 4 and the sum of their ages is 28, then find the age of B.
Three boys, on an average, are 25 years old, and their age are in the ratio of 3 : 5 : 7.
What is the age of youngest boy'?
Six years ago, the ratio of ages of A to B was 7 : 5. After 4 years from now, the ratio of their ages will be 11 : 9. What is A’s age at present?
Gautam’s present age is equal to 20% of his father's age 15 years ago, and Gaurav's (brother of Gautam) present age is 60% of his father’s age 10 years ago. If the sum of Gautam’s present age and Gaurav’s present age is 31, then find their father’s present age.
Sum of current age of vishal and Aditi is 25 years younger than vishal , then what will be the present age of Pritam , who is 7 years older than Aditi
Seven years ago, the ratio of the ages of A and B was 4 : 5. Eight years hence, the ratio of the ages of A and B will be 9 : 10. What is the difference between their present ages in years?
The present ages of A and arein the ratio 3 : 4. Twelve years ago, their ages were in the ratio 2 : 3. The sum of the present agesofA andB (in years)is:
Seven years from now, Anamika will be as old as Malini was 4 years ago. Srinidhi wasborn 2 years ago. The average age of Anamika, Malini and Srinidhi 10 years from nowwill be 33 years. What is the present age of Anamika?
The present age of Ramesh is 7 years more than the present age of his wife Sangeeta. 6 years hence, the age of Ramesh will be three times that of his son Mayank. If the present age of Mayank is 10 years, then what is the present age of Sangeeta?
Alekhya was born one year after her mother's marriage. Her father is two years elder than her mother but twenty five years older than Alekhya, who is six years old. At what age did
the mother get married?
The average age of 17 persons is 39 years. If the average age of the first 9 persons is 35 years, and the average age of the last 9 persons is 44 years, what is the age of the 9th person?
Thetotal of the ages of four persons is 86 years. What was their average age 4 years ago?
One mother told her son, ‘’When you were born, my age was the same as your present age’’. If 5 years ago, the age of a son is 16 years, then find out the present age of the mother.
The father of a girl is three years older than his mother. Six years ago, the average age of the girl and her parents was 32 years, and the age of the father was twice the present age of his daughter. What is the present age (in years) of the mother?
Eight years ago, the ratio of the ages of A and B was 4:5 and the ratio of their ages, 12 years hence. will be 13 : 15. The present age (in years) of B is:
Ratio of the present age of a motherto that of the daughteris 7 : 1. After 5 years the ratio will become 4 : 1. What is the difference (in years) in their present ages?
The average age of Akhil and Sunita is 51 years, of Sunita and Veena is 31 years, and that of Veena and Akhil is 33 years. The age of Veena is:
Twelve years ago, the ratio of the ages of Anil and Bishu was 5: 12, Eight years from now, the ratio of their ages will be 10 : 17. What is the ratio of the present ages of Anil and Bishu?
Vineeth is younger than Vinoth by 8 years. If 4 years ago, their ages were in the ratio of 1 : 2, then the present age of Vinoth is:
Seven years ago, the ratio of the ages of A and B was 2 : 3. Three years hence, the ratio of their ages will be 5 : 7. The sum of their present ages (in years) is:
The ratio of present ages of A and is 7 : 8. After 6 years from now, the ratio of their ages will be 8 : 9. If C's present age is 10 years more than the presentage of A, then the present age (in years) of C is:
Twelve years ago, the ratio of the ages of A and B was 12 : 5. Twelve years from now, the ratio of their ages will be 18 : 11 . What is the difference between their present ages (in years)?
If A is one third of B, B is twice of C, D is two-third of A and the average of A, B, C and D is 74, then the difference between A and C is:
The ratio of the present ages of A and B is 6:5. Four years ago, this ratio was 5:4. What will be the ratio of the ages of A and B after ten years?
The ratio of the present ages of a mother and daughter is 3 : 1. Five years ago, the ratio of their ages was 5 : 1. Find the age of the mother 41 years hence.
The present age of a father is three times that of his elder son. Four years hence, the age of the father will be four times that of his younger son. If the difference between the present
ages of the elder and younger child is 6 years, what is the present age of the father?
The present ages of a mother and her son are in the ratio of 6 : 1. When the son becomes as old as his mother now, then the ratio of his father's age to his mother's age is 13 : 11. When the son becomes as old as his father now, then the sum of the ages of the father and son will be 115 years. The present age of the father is:
The average age of two persons 5 years ago was 7.5 years. Find their average age after 5 years.
Three years ago, the average age of A, B and C was 29 years. If the average age of B and C, 5 years ago, was 23 years, then what is the present age (in years) of A?
Akshar and Manvita recently celebrated their silver wedding anniversary and their older son Sanju’s birthday. If the age of Sanju 18 years after his parent’s marriage, and his age at their golden anniversary is in the ratio 5 : 21, how many years after their marriage was Sanju born?
The average age of husband, wife and child 7 years ago was 42 years and that of wife and child 9 years ago was 36 years. The presentage of the husband is:
Let the present age of husband = $$x$$
the present age of wife =$$y$$
and the present age of child = $$z$$
then according to question, $$\dfrac{(x-7)+(y-7)+(z-7)}{3} = 42 $$
$$\Rightarrow x+y+z = 126 + 21$$
$$\Rightarrow x +y +z = 147 $$ ......... equestion (1)
again according to question $$\dfrac { (y-9) + (z-9)} {2} = 36 $$
$$\Rightarrow y +z -18 = 72 $$
$$\Rightarrow y +z = 90 $$ ........... equestion (2)
so equestion (2) subtract from equestion (1)
then $$x +y + z - y -z = 147 - 90 $$
$$\Rightarrow x = 57 $$
then the present age of husband = 57 Ans
Seven years ago, the ages (in years) of A and B were in the ratio 4 : 5 and 7 years hence, their ages will be in the ratio 5 : 6. What will be the ratio of their ages 5 years from now?
Let Age of A = a, And ages B = b
then according to question $$\dfrac {a-7}{b-7} = \dfrac {4}{5}$$
$$\Rightarrow 5a - 35 = 4b - 28 $$
$$\Rightarrow 5a -4b = 7 $$ ........ equestion (A)
again second case $$\dfrac{a + 7 }{b+7} = \dfrac {5} {6} $$
$$\Rightarrow 6a + 42 = 5b + 35 $$
$$\Rightarrow 6a - 5b = 7 $$ ......... equestion (B)
then Substract B from A
so $$ 5a - 4b + 6a - 5b = 0 $$
$$\Rightarrow 11 a = 9b $$
$$\Rightarrow a = \dfrac {9}{11}b $$ ...... equestion (C)
put the value in the equestion B
so 55 b - 54b = 77
b = 77 so we put the value of b = 77 in equestion (C)
$$a = \dfrac {9}{11}\times 77 $$
a = 63
then again $$\dfrac {a +5}{b+ 5}$$
$$\Rightarrow \dfrac {63+5}{77 +5}$$
$$\Rightarrow \dfrac {68}{82}$$
$$\Rightarrow \dfrac {34}{41}$$ Ans
A group of three friends, K, L and M, are sitting in a cafe. Their average age is 24 years. Another friend ‘N’ joins the group and the new average age of the group becomes 23 years. If another friend ‘R’, whose age is 2 years more than that of ‘N’, replaces ‘K’, then the average age of L. M, N and R becomes 22.5 years. What is the age of K?
Average of K, L and M = 24
Sum of the age of K, L and M = 24 $$\times$$ 3 = 72
Average of K, L, M and N = 23
Sum of the age of K, L, M and N = 23 $$\times$$ 4 = 92
Age of N = 92 - 72 = 10
Age of R = 2 + Age of N = 2 +10 = 12
Average age of L, M, N and R = 22.5 years
Sum of age of L, M, N and R = 22.5 $$\times$$ 4 = 90
Sum of age of L, M and N = 90 - 12 = 78
Age of K = sum of the age of K, L, M and N - sum of age of L, M and N = 92 - 78 = 14
Afather’s age is 3 timesofhis son’s age at present. 10 years back, the father’s age was 5 timesofhis son’s age. Whatis the age of the son at present ?
Let F and S be the present ages of the father and son respectively.
F = 3*S
F - 10 = 5*(S - 10)
3S - 10 = 5S - 50
2S = 40
S = 20 years
The ratio of the ages ofA and B, 8 years ago, was 2 : 3. Four years ago,the ratio of their ages was 5 : 7. What will be the ratio of their ages 8 years from now?
8 years ago the ratio of the ages of A and B = 2 : 3
Let the 8 years ago ages of A and B be 2x and 3x respectively.
4 years age of A = 2x + 4
4 years agoof B = 3x + 4
Four years ago,the ratio of their ages = 5 : 7
$$\frac{2x + 4}{3x + 4} = \frac{5}{7}$$
14x + 28 = 15x + 20
x = 8
8 years from now, Age of A = 2x + 16 = 2$$\times$$8 + 16 = 32
8 years from now, Age of B = 3x + 16 = 3$$\times$$8 + 16 = 40
Ratio of their ages 8 years from now = 32 : 40 = 4 : 5
The average age of A, B and C is 20 years, and that of B and C is 25 years. What is the age of A?
Given, the average age of A, B and C is 20 years
$$\Rightarrow$$ Sum of the ages of A, B and C = 20 x 3 = 60 years
$$\Rightarrow$$ A + B + C = 60 ..........(1)
Average age of B and C is 25 years
$$\Rightarrow$$ Sum of the ages of B and C = 25 x 2 = 50 years
$$\Rightarrow$$ B + C = 50 ..............(2)
From (1) and (2), A = 10 years
$$\therefore\ $$Age of A = 10 years
Hence, the correct answer is Option B
The total of the ages ofAmit and Suvarna on 1 January 2015 is 61 years. Amit is three years younger than Suvarna. What was the age of Survarna on 1 January 2010?
Age of Amit + 3 = age of Suvarna
The total of the ages of Amit and Suvarna on 1 January 2015 = 61 years
Age of Amit + Age of Suvarna = 61 years
Age of Amit + Age of Amit + 3 = 61
Age of Amit = 58/2 = 29 years
Age of Suvarna on 1 January 2015 = age of Amit + 3 = 29 + 3 = 32
Age of Survarna on 1 January 2010 = 32 - 5 = 27 years
$$\therefore$$ The correct answer is option A.
10 years ago. a father's age was $$3\frac{1}{2}$$ times that of his son, and 10 years from now, the fathers age will be $$2\frac{1}{4}$$ times that of the son. What will be the sum of the ages of the father and the son at present?
Let the present age of the son is x years and father's age is y years.
10 Year before, the age of the son was =x-10 and age of father =y-10
As per the condition given in the question,
$$y-10=\dfrac{7(x-10)}{2}$$
$$\Rightarrow 2y-20=7x-70$$
$$\Rightarrow 7x-2y=50------(i)$$
Now, The age of son after 10 year, will be $$x+10$$ and father's age $$=y+10$$
as per the given condition in the question,
$$\Rightarrow y+10=\dfrac{9(x+10)}{4}$$
$$\Rightarrow 4y+40=9x+90$$
$$\Rightarrow 9x-4y=-50 ------(ii)$$
From the equation (i) and (ii),
$$x=30years$$ and $$y=80years$$
Hence the sum of the age=$$80+30=110$$years
5 years ago, the ratio of the age of A to that of B was 4 : 5. Five years hence, the ratio of the age of A to that of B will be 6 : 7. If, at present, C is 10 years younger than B, then what will be the ratio of the present age of A to that of C?
5 years ago, the ratio of the age of A to B = 4 : 5
Let 5 years ago, the age of A and B be 4x and 5x.
Five years hence, the ratio of the age of A to B = 6 : 7
ATQ,
$$\frac{4x + 10}{5x + 10} = \frac{6}{7}$$
28x + 70 = 30x + 60
2x = 10
x = 5
Present age of A = 4x + 5 = 4 $$\times$$ 5 + 5 = 25
Present age of B = 5x + 5 = 5 $$\times$$ 5 + 5 = 30
Present age of C = 30 - 10 = 20
Ratio of the present age of A to that of C = 25 : 20 = 5 : 4
Vishal is three times as old as Saksham. After 8 years, he will be two times as old as Saksham. After further 8 years, what will be Vishal’s age?
Assume Saksham's age = x
So Vishal's age = $$3x$$
After 8 years
$$3x + 8 = 2(x+8)$$
x = 8
so 3x = 24
after further 8 years age of vishal = 24+8= 32
A father was twelve times as old as his son twenty years ago. Now he is twice as old as his son. What are the present ages ofthe son and father?
Ina school, $$\frac{4}{9}$$ of the numberof students are girls and the rest are boys. $$\frac{3}{5}$$ of the number of boys are below 12 years of age and $$\frac{5}{12}$$ of the number of girls are 12 years or above 12 years of age. If the number of students below 12 years of age is 480, then $$\frac{5}{18}$$ of the total number of students in the school will be equal to:
Let the total student be x.
Number of girls = 4x/9
Number of boys = x - 4x/9 = 5x/9
Number of boys below 12 years = 5x/9 $$\times$$ 3/5 = x/3
Number of girls are 12 years or above 12 years of age = 4x/9 $$\times$$ 5/12 = 5x/27
Number of girls below 12 years = $$\frac{4x}{9} - \frac{5x}{27}$$ = 7x/27
The number of students below 12 years of age = 480
Number of boys below 12 years + number of girls below 12 years = 480
$$\frac{x}{3} +\frac{7x}{27}$$ = 480
16x/27 = 480
x = 810
$$\frac{5}{18}$$ of the total number of students in the school = 810 $$\times \frac{5}{18}$$ = 225
The sum of the current ages of Vinayak and his father is 50 years. 5 years from now, Vinayak’s age will be one-fifth of his father’s age. Whatis Vinayak’s current age?
Let the Vinayak's age be x and his father's age be y
x+y=50
x=50-y
According to the question,
$$\frac{1}{5}\left(y+5\right)=x+5$$
$$\frac{y}{5}+1=x+5$$
$$\frac{y}{5}-x=4$$
$$\frac{y}{5}-\left(50-y\right)=4$$
$$\frac{y}{5}+y=54$$
$$y=45$$
Vinayak's age = 5 years.
The sum of the current ages of Vishal and Armaan is 70 years. 5 years ago, Vishal was twice as old as Armaan. What is Armaan’s current age?
Let the current age of Arman=x Years and age of Vishal = Y years
As per the question,
$$x+y=70------(i)$$
5 Years ago, age of Vishal =Y-5
5 Years ago, age of Arman= x-5
As per the condition,
$$\Rightarrow 2(x-5)=(y-5)$$
$$\Rightarrow 2x-10=y-5$$
$$\Rightarrow 2x-y=10-5=5$$
$$\Rightarrow 2x-y=5--------------(ii)$$
From the equation (i) and (ii)
$$\Rightarrow 3x=75$$
$$\Rightarrow x=25$$ Years
So, $$y=45$$Years
Hence current age of Arman =25 Years.
An employer reduces the number of his employees in the ration 9 : 8 and increases their wages in the ration 14 :15. If the original wage was Rs, 18,900, find the ratio in which the wage bill is decreased
original number of employees = 9x
present number of employees = 8x
original wages = 14y
present wages = 15y
let original wage bill = $$ 9x \times 14y = 126xy $$
present wage bill = $$ 8x \times 15y = 120xy $$
wage bill ratio original : present = 126xy : 120xy = 21 : 20
thus wage bill decreased in the ratio 21 : 20
The sum of the current ages of Asma and her grand father is 80 years. 10 years from now, Asma’s age will be one-fourth of her grandfather’s age. What is Asma’s current age?
Let Asma's age$$ = x$$
So, the age of grandfather of Asma $$=80-x$$
The age of Asma after 10 years will be $$=x+10$$
So, the age of grandfather of Asma $$=80-x+10=90-x$$
As per the condition is given in the question,
$$\Rightarrow x+10=\dfrac{90-x}{4}$$
$$\Rightarrow 4x+40=90-x$$
$$\Rightarrow 4x+x=90-40=50$$
$$\Rightarrow x=\dfrac{50}{5}=10$$
Hence, Asma's current age =10 Years.
7 years ago, the ages (in years) of A and B were in the ratio 4 : 5; and 7 years hence they will be in the ratio 5 : 6. The present age of B is
7 years ago, the ages of A and B were in the ratio 4x : 5x
7 years hence they will be in the ratio 5x : 6x
forming the equation
4x + 7 = 5x - 7
solving we get x = 14
therefore age of B 7 years ago = $$ 14 \times 5 = 70 $$
present age of B = 70 + 7 = 77
Nisha and Deepak are a married couple and have a daughter named Tanya. Currently, Deepak is 5 years older than Nisha and Nishais thrice the age of Tanya. If Tanya is 10 years old, what washer father’s age at the time of his daughter’s birth?
GIVEN that TANYA IS 10 YEARS OLD ,and NISHA IS THRICE OF TANYA
LET NISHA'S AGE IS "X"
DEEPAK IS= X+5
SO , AS GIVEN NISHA IS THRICE OF TANYA THAT IS $$3\times10 =30$$
DEEPAK AGE IS 30+5 = 35 .
FATHERS AGE IS AT THE TIME OF DAUGHTERS BIRTH : 35-10 = 25.
The ratio of the present age of Mitali to that of Shabnam is 4 : 7. If the difference between the present ages of Shabnam and Mitali after 5 years will be 13 years, then what is the sum of the present ages of Mitali and Shabnam?
The sum of the current ages of Natasha and Krishna is 50 years. 10 years ago, Krishna was twice as old as Natasha. What is Krishna’s current age?
Option D is correct,
Let us take the present age of Natasha is x and the present age of Krishna is y. So that,
x+y=50 ----- (i)
y=50-x
Ten year ago, Krishna was twice as old as Natasha so that,
(y-10)=2(x-10)
put the value of y
(50-x-10)=2x-20
from solving the equation we get
x=20
Put the value of x in equation (i)
20+y=50
y=30
So the present age of Krishna is 30 years.
A man can finish a piece of work in 15 days. A woman can complete the same work in 10 days. Both work together for 5 days, then the man leaves. How many days will be taken by the woman tofinish the remaining work?
The man's 1 day's work = $$ \frac {1} {15}
The woman's 1 day's work = $$ \frac {1} {10}
1 day's work done by both man and woman together = $$ \frac {1} {15} + $$ \frac {1} {10}
= $$\frac {(2+3)}{30}$$
= $$ \frac {5}{30}$$
= $$ \frac {1}{6}$$
They work together for 5 days. Hence the work done by both man and woman together = 5 $$ \times \frac {1}{6} $$ = $$ \frac {5}{6}$$
Remaining work left = 1 - $$ \frac {5}{6}$$ = $$ \frac {1}{6}$$So, this work will be completed by the woman as men left after working for 5 days.
Hence 10 women will take to complete = 10 x $$ \frac {1}{6}$$ = $$ \frac {10}{6}$$ = $$ \frac {5}{3}$$ = 1 $$ \frac {2}{3}$$
The average age of 3 persons is 30 years.If their ages are in the ratio of 3:5:7 respectively, then the age ofthe eldest person is:
Given average age of three persons =30 years
Sum of the ages of three people=90 years
let the ages of three people be 3x,5x and 12x.
sum=3x+5x+7x
=15x
15x=90
x=6
Age of eldest person=7*6
=42 years
The present ages of A and are in the ratio 15 : 8. After 8 years their ages will be in the ratio 17 : 10. What will be the ratio of ages of A and B after 10 years from now?
Let present age of A = $$15x$$ years and B = $$8x$$ years
According to ques,
=> $$\frac{15x+8}{8x+8}=\frac{17}{10}$$
=> $$150x+80=136x+136$$
=> $$14x=136-80=56$$
=> $$x=\frac{56}{14}=4$$
$$\therefore$$ Ratio of ages of A and B after 10 years from now = $$\frac{15\times4+10}{8\times4+10}$$
= $$\frac{70}{42}=5:3$$
=> Ans - (C)
Age of A is 6 years more than three times the age of B. After three years, A's age will be 8 years more than twice the age of B. The average of present ages of A and (in years) is:
Let the present age of B = x
A B
Present Age 3x+6 x
After 3 years 3x+6+3 = 3x+9 x+3
Given, After 3 years A's age will be 8 years more than twice the age of B
$$=$$> 3x+9 = 2(x+3)+8
3x+9 = 2x+6+8
x = 5
Average of Present ages of A and B = $$\ \frac{\ 3x+6+x}{2}$$
= $$\ \frac{\ 4x+6}{2}$$
= $$\ \frac{\ 4\left(5\right)+6}{2}$$
= 13
The sum of the present ages of a father and his son is 78 years. After five years, the ratio of their ages becomes 7 : 4. What is the present age (in years) of the father?
Given,
Sum of present ages of father and son is 78 and their ratio after 5 years is 7:4
let the age of father and son after 5 years be 7x and 4x
sum of the present ages can be written as,
(7x-5) + (4x-5) = 78
7x + 4x - 10 = 78
11x - 10 = 78
11x = 88
x = 8
The age of father after 5 years is $${7}\times{8}$$ = 56
therefore the present age of father is 56 - 5 = 51
The present age of a Manoj is twice the sum of the ages of his two children. After 20 years, the age of Manoj will become equal to the sum of the ages of his two children. Whatis the present age of Manoj?
Let Present Age of Manoj = m
Sum of Present ages of two children = s
Given, Present Age of Manoj is twice the sum of both children
$$=$$> m= 2s ..................(1)
After 20 years, Sum of Ages of two children = s+20+20
= s+40
According to Problem, After 20 years age of Manoj is equal to the Sum of Ages of both children
$$=$$> m+20 = s+40
m = s+20............(2)
From equations (1) and (2)
2s = s+20
s = 20
Therefore, Present Age of Manoj = 2m
= 2$$\times\ $$20
= 40 years
The ratio of the ages of A and B. four years ago. was 4 : 5, Eight years from now, the ratio of the ages of A and B will be 11 : 13. What is the sum of their present ages?
Four years ago ,
$$\frac{A' age}{B' age}$$ = $$\frac{4}{5}$$
Suppose A' age = 4x and B's age= 5x
Eight years later ,
$$\frac{A' age}{B' age}$$ = $$\frac{11}{13}$$
$$\frac{4x + 12}{5x + 12}$$ = $$\frac{11}{13}$$
52x + 156 = 55x + 132
x = 24 / 3 = 8
Present ages of A = 4x + 4 = 36 and B = 5x + 4 = 44
Sum of their present ages = 80
So , the answer would be option a)80.
Five years ago, the ratio of the ages of A and B was 3 4. Five years from now,the ratio of their ages will be 4 : 5. What is the ratio of A and B, 10 years from now?
Let the ages of A and B are 3p and 4p five years ago respectively
A B
5 years ago 3p 4p
After 5 years 3p+10 4p+10
After 10 years 3p+15 4p+15
Given ratio of ages of A and B after 5 years is 4:5
$$=$$> $$\ \frac{\ 3p+10}{4p+10}=\ \frac{\ 4}{5}$$
$$\ \ 15p+50=\ 16p+40$$
$$p=10$$
Therefore ratio of ages of A and B after 10 years = 3p+15: 4p+15
= 3(10)+15 : 4(10)+15
= 45:55
= 9:11
Five years ago, the average age of four girls, was 7 years. A new girl is included then the average present age becomes 13 years. The present age of the new girl is:
Five years ago, the average age of four girls = 7
Sum of the ages of the four girls = 7$$\times\ $$4= 28
Sum of the present ages of four girls = 28+20= 48
Let the present age of new girl = $$x$$
Average of the present ages of five girls = 13
$$=$$> $$\ \frac{\ 48+x}{5}=13$$
$$\ \ x=65-48=17$$
Ramesh is thrice as old as Suresh. Two years hence, Ramesh will be twice as old as Suresh. Ramesh’s present age (in years) is:
Ramesh Suresh
Present Age 3x x
After 2 years 3x+2 x+2
Given 3x+2 = 2(x+2)
3x+2 = 2x+4
x = 2Therefore, Ramesh Present Age = 3x
= 3 x 2
= 6 years
The ratio of ages of A and B, 4 years ago, was 5 : 7. The ratio of their ages after 4 years from now will be 7 : 9. What will be the ratio of ages of A and B after 12 years from now?
Let ages of A and B 4 years age be $$5x$$ and $$7x$$ years respectively.
=> Ratio of ages 4 years from now (i.e. 8 years from then) = $$\frac{5x+8}{7x+8}=\frac{7}{9}$$
=> $$45x+72=49x+56$$
=> $$4x=16$$
=> $$x=4$$
Ratio of ages 12 years from now = $$\frac{5(4)+16}{7(4)+16}=\frac{36}{44}$$
= $$9:11$$
=> Ans - (C)
The ratio of the present ages of A and is 8 : 15. Eight years ago,the ratio of their ages was 6 : 13. What will be the ratio of ages of A and B after 8 years from now?
The ratio of the present ages of Meera and Sheela is 9 : 5. After 8 years Sheela would reach the present age of Meera. What is the present age (in years) of Sheela?
Let present ages of Meera and Sheela be $$9x$$ and $$5x$$ years respectively.
According to ques, => $$9x=5x+8$$
=> $$9x-5x=4x=8$$
=> $$x=2$$
$$\therefore$$ Present age of Sheela = $$5\times2=10$$ years
=> Ans - (B)
A family consists of two grandparents, three parents and four grandchildren. The average age of the grand parents is 65 years, that of the parents is 32 years and that of the grand children is 8 years. What is the average age of the family?
Given 2 grandparents average as 65 so sum of their ages=65*2=130 years
Also given 3 parents average as 32 so sum of their ages=32*3=96 years
Also given 4 grandchildren average as 8 so sum of their ages=8*4=32 years
Total sum of ages=130+96+32=258 years
Average=258/9
=86/3 years
A family consists of two grandparents, two parents and four children. Two years ago, the average age of the grandparents was 72 years. One year ago, the average age ofparents was 36 years. At present, the average age of the children is 12 years. Whatis the present average age of the family?
Two years ago, Average age of two grandparents = 72 years
Sum of the ages of two grandparents = 72$$\times\ $$2= 144
Sum of Present ages of two grandparents = 144+2+2=148
One year ago, Average age of two parents = 36 years
Sum of the ages of two parents = 36$$\times\ $$2= 72
Sum of Present ages of two parents = 72+1+1=74
Present average age of four children = 12 years
Sum of Present ages of four children = 12$$\times\ $$4= 48
Present average age of family = $$\ \frac{\ 148+74+48}{2+2+4}$$= $$\ \frac{\ 270}{8}$$= 33.75 years
Five years ago, the ratio of the ages of a father and his son was 5 : 3. Which ofthe following cannotbethe ratio of their ages 10 years from now?
Five years ago, the ratio of the ages of a father and his son was 5 : 3.
As we know that when time progresses the ratio between the ages always decreases.
$$Ratio of age_{5 years ago} > Ratio of Present age > Ratio of age_{5 years later}$$
Option D violates this. $$[\frac{7}{3} > \frac{5}{3}]$$
Option D is correct.
Kartik’s father age is four times the age of Kartik. Three years ago, Kartik’s father age was seven times the age of Kartik. The present age of Kartik is:
Let the age of Karthik = p
Karthik's Father Karthik
Present Age 4p p
Three years ago 4p-3 p-3
Given, Three years Karthik's Father age was seven times the age of Karthik
$$=$$> 4p-3 = 7(p-3)
4p-3 = 7p-21
3p = 18
p = 6
One year ago, the ratio of the age (in years) ofA to that of B was4 : 3. The ratio of their respective ages, 3 years from now,will be 6 : 5. What will be the ratio of respective ages of A and B, 9 years from now?
One year ago, the ratio of the age (in years) of A to that of B = 4 : 3
After 3 year, the ratio of the age (in years) of A to that of B = 6 : 5
After 3 year, let the age of A and B are 6x and 5x.
ATQ,
$$\frac{4x + 4}{3x + 4} = \frac{6}{5}$$
20x + 20 = 18x + 24
2x = 4
x = 2
After 9 year, the ratio of the age (in years) of A to that of B = 6x + 6 : 5x + 6
6 $$\times$$ 2 + 6 : 5 $$\times$$ 2 + 6 = 18 : 16 = 9 : 8
Ravi’s age is $$\frac{3}{5}$$ of Shyam’s age. After x years the ratio of the ages of Ravi and Shyam becomes 5 : 7. If initially the sum of their ages is 32, then what is the value of x ?
Let Present Age of Shyam = s then
Present Age of Ravi = $$\ \frac{\ 3}{5}$$s
Given Sum of ages of Ravi and Shyam is 32
$$=$$> $$\ \frac{\ 3}{5}s+s=32$$
$$\ \frac{\ 8}{5}s=32$$
$$\ s=20$$
Present Age of Shyam = 20
Present Age of Ravi = $$\ \frac{\ 3}{5}\times\ 20$$
= 12
After 'x' years the ratio of ages of Ravi and Shyam = 5:7
$$=$$> $$\ \frac{12+x\ }{20+x}=\ \frac{\ 5}{7}$$
$$84+7x=100+5x$$
$$2x=16$$
$$x=8$$
The current age of Savan is four times the age of Akshan. 10 years from now, Savan’s age will be twice the age of Akshan. What is Savan’s current age?
Let Savan ' age be s and Akshan be a.
A/c to question ,
s = 4a
10 years later ,
s + 10 = 2(a + 10)
Solving these two questions , a = 5
s = 20
So , the answer would be option b)20.
The ratio of the age of a father and his sonis 3 : 1. If the product of their ages is 432, then whatis the sum oftheir ages?
Let Age of the son = s
$$=$$> Age of the father = 3s
GIven Product of their ages = 432
$$=$$> 3s $$\times\ $$ s = 432
3$$s^2$$ = 432
$$s^2$$ = 144
s = 12
Sum of their Ages = s+3s
= 4s
= 4$$\times\ $$12
= 48 years
The ratio of ages of A and B, four years ago, was $$7 : 5$$. The ratio of their ages, 6 years from now, will be $$19 : 15$$. What is the ratio of the present ages of A and B?
Let the ages of A and B four years ago are 7p and 5p respectively
A B
4 years ago 7p 5p
Present age 7p+4 5p+4
after 6 years 7p+10 5p+10
Given ratio of their ages after 6 years = 19:15
$$=$$> $$\ \frac{\ 7p+10}{5p+10}=\ \frac{\ 19}{15}$$
$$105p+150=95p+190$$
$$10p=40$$
$$p=4$$
Ratio of present ages of A and B = 7p+4 : 5p+4
= 32 : 24
= 4 : 3
The average age of husband, wife and their child 4 years ago was 26 years and that of wife and child 3 years ago was 22 years. What is the present age of the husband?
Let the present ages of Husband, Wife and Child be H, W and C years respectively.
Given, $$\dfrac{H-4+W-4+C-4}{3} = 26 => H+W+C-12 = 78 => H+W+C = 90$$
$$\dfrac{W-3+C-3}{2} = 22 => W+C - 6 = 44 => W+C = 50$$
Substituting W+C = 50 in above equation.
H+50 = 90 => H = 40
Therefore, The present age of the husband = 40 years.
The ratio of the present age of Mahesh and Ajay is 3 : 2 respectively. After 8 years. Ratio of their age will be 11: 8. What will be the present age of Mahesh’s son if his age is half of the present age of Ajay?
Let the present ages of Mahesh and Ajay be 3x years and 2x years respectively.
Then, Their ages after 8 years will be 3x+8 years and 2x+8 years.
Given, $$\dfrac{3x+8}{2x+8} = \dfrac{11}{8}$$
$$24x+64 = 22x+88$$
=> $$2x = 24$$
=> $$x = 12$$
Then, Present ages of Mahesh and Ajay are 36 years and 24 years respectively.
Present age of Mahesh's son = Half of Present age of Ajay = 12 years.
The ratio of the present ages of A and B is 8: 9. After 9 years, this ratio will become 19: 21. C is 3 years younger to B. What is the present age (in years) of C?
Let the present age of A and B is x and y.
Given that the ratio of the age of A and B, $$\dfrac{x}{y}=\dfrac{8}{9}$$
$$x=\dfrac{8y}{9}-------------(i)$$
After 9 years, age of A=x+9 and age of B=y+9,
The ratio in the age after 9 years,
$$\dfrac{x+9}{y+9}=\dfrac{19}{21}-------------(ii)$$
From equation (i) and (ii)
$$\Rightarrow \dfrac{ \dfrac{8y}{9} +9}{y+9}=\dfrac{19}{21}$$
$$\Rightarrow \dfrac{ 8y+81}{9(y+9)}=\dfrac{19}{21}$$
$$\Rightarrow \dfrac{ 8y+81}{9y+81}=\dfrac{19}{21}$$
$$\Rightarrow 21 \times 8y+21\times 81=19\times9y+19\times 81$$
$$\Rightarrow 168y+21\times 81=171y+19\times 81$$
$$\Rightarrow 171y-168y=21\times y -19\times 81$$
$$\Rightarrow 3y=2\times 81$$
$$\Rightarrow y=54$$years
Hence the age of C $$=y-3=51$$Years.
The ratio of the present ages of a mother and a son is 4: 1. Fourteen years from now, the ratio of their ages will be 2 : 1 The present age (in years) of mother is:
Mother Son
Present 4p 1p
After 14 years 4p+14 1p+14
Given $$\ \frac{\ 4p+14}{1p+14}=\ \frac{\ 2}{1}$$
4p+14 = 2p +28
2p = 14
p = 7
Present Age of Mother = 4p = 4 x 7 = 28 years
The ratio of the ages of two persons is 3 : 4. If the age of one of them is greater than the other by 8 years, then what is the sum of their ages?
Let the ages of both the persons to be x and y. Then,
$$\frac{x}{y}$$=$$\frac{3}{4}$$
x =3$$\times\frac{y}{4}$$,
x = y-8
putting x value in the given equation. so y-8 = 3$$\times\frac{y}{4}$$
$$\frac{y}{4}$$ = 8
y = 32
x = y-8 = 32-8 = 24
Hence total ages of x and y = 24 +32= 56.
The ratio of the ages of Arun and Anand is 3:1. After 5 years Arun age will be 5 more than two times of Anand’s age. Then the present age of Arun is
Let the ages of Arun and Anand be 3x and x
After 5 years Arun's age=3x+5 and Anand's age=x+5
Given 3x+5=2(x+5)+5
3x+5=2x+10+5
x=10
Present age of Arun=30 years
The ratio of present ages of Rahul and his sister is 3 : 4. Before 10 years the ratio of their ages was 13:19. What is Rahul's present age (in years)?
Assuming, present age of Rahul= x years and his sister= y years.
So, Present ratio= $$x\div y= 3\div4$$ .....(i)
Before 10 years the ratio of their ages
=$$(x-10)\div (y-10)= 13\div19$$ ......(ii)
Solving equation (i) & (ii),
We get, x=36 years and y=48 years.
Therefore, Option A is correct.
The ratio of present ages of Simi and Seema is 5 : 4. After 9 years the ratio of their ages will be 8 : 7. What is Simi's present age (in years)?
Let say, Simi and Seema's present age is 5k and 4k.
So, (5k+9)/(4k+9)=8/7 .
or, 35k+63=32k+72 .
or, 3k=9.
or, k=3 .
Simi's present age=5×3=15.
B is correct choice.
The sum of the current ages of Shipra and Malini is 65 years. After 5 years, Shipra’s age will be 15 years more than Malini’s age. What is Malini’s current age?
Let the age of Shipra be s and Malini be m.
s + m = 65 ----(1)
After 5 years ,
s + 5 = m + 5 + 15
s - m =15-----(2)
Solving (1) and (2) , we get ,
s = 40 and m = 25
So , the answer would be option a)25 years.
The ratio of ages of the father and mother was 11:10 when their son was born. The ratio of ages of the father and mother will be 19:18 when the son will be twice his present age. What is the ratio of present ages of father and mother?
Ratio of parents present age is 11:10 And the ratio of ages of the father and mother will be 19:18 when the son will be twice his present age
Let the present age of son be x
Then the twice age will be 2x
According to question:
$$\frac{11 + 2x}{10 + 2x} = \frac{19}{18}$$
$$18(11 + 2x) = 19(10 + 2x)$$
$$198 + 36x = 190 + 38x$$
$$8 = 2x$$
$$x = 4$$
Ratio of present ages will be:
$$\frac{11 + x}{10 + x} = \frac{11 + 4}{10 + 4}$$
Required ratio is: (15/14).
A is correct choice.
Ravi is 12 years younger than Surya. Ravi's age is 40% of the sum of his and Surya's age. What will be Surya's age 9 years hence?
let surya's age=s
ravi's age=r
Given s-r=12
r=0.4(r+s)
0.6r=0.4s
0.6(s-12)=0.4s
0.6s-7.2=0.4s
0.2s=7.2
s=36 yers
9 years from now age will be 36+9=45 years
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Let present age of husband, wife and child be $$h,w,c$$ years respectively.
Average age of husband, wife and their child 3 years ago = 27 years
=> Total present ages of husband, wife and their child = $$(27+3)\times3$$
=> $$h+w+c=90$$ ---------(i)
Similarly, present age of wife and the child = $$(20+5)\times2$$
=> $$w+c=50$$
Subtracting equation (ii) from (i), we get :
=> $$h=90-50=40$$
$$\therefore$$ The present age of the husband = 40 years
=> Ans - (B)
The present ages of A and B are in the ratio 5 : 6 respectively. After seven years this ratio becomes 6: 7. Then the present age of A in years is:
Let present age of A = $$5x$$ years and B = $$6x$$ years
According to ques,
=> $$\frac{5x+7}{6x+7}=\frac{6}{7}$$
=> $$35x+49=36x+42$$
=> $$36x-35x=49-42$$
=> $$x=7$$
$$\therefore$$ Present age of A = $$5\times7=35$$ years
=> Ans - (A)
The ratio of present ages of Raman and Lamba is 7 : 5. After 6 years, age of Raman will be 48 years. What is the present age (in years) of Lamba?
It is given that 6 years hence, Raman's age = $$48$$ years
=> Raman's present age = $$48-6 = 42$$ years
Ratio of present ages of Raman and Lamba = 7 : 5
=> Lamba's present age = $$\frac{5}{7}\times42=30$$ years
=> Ans - (A)
M is 2 years older than P. L is 2 years older than O. O's age is the average of the ages of L and N, P's age is the average of the ages of L and M and L's age is the average of P and O. Who is the youngest?
Given,
M is 2 years older than P.
$$\Rightarrow$$ M > P
L is 2 years older than O
$$\Rightarrow$$ L > O
O's age is the average of the ages of L and N which means O's age lies between L and N.
$$\Rightarrow$$ L > O > N ...........(1)
P's age is the average of the ages of L and M which means P's age lies between L and M.
$$\Rightarrow$$ M > P > L ...........(2)
Combining (1) and (2)
M > P > L > O > N
$$\therefore\ $$N is the youngest person
Hence, the correct answer is Option C
Present age of P is 45 years. 9 years hence ages of P and Q will be in ratio 6 : 7. What is the present age (in years) of Q?
Let P's and Q's age 9 years hence = $$6x$$ and $$7x$$ years respectively.
=> P's present age = $$6x-9=45$$
=> $$6x=45+9=54$$
=> $$x=\frac{54}{6}=9$$
$$\therefore$$ Q's present age = $$7x-9$$
= $$7(9)-9=63-9=54$$ years
=> Ans - (B)
Present ages of Richa and her husband are in ratio 3 : 4. Five years from now, ages of her husband and her son will be in ratio 3 : 1. If the present age of Richa is 21 years, then what will be her son’s present age (in years)?
Let Richa's present age = $$3x$$ years and her husband's present age = $$4x$$ years
Also, present age of Richa = 21 years
=> $$3x=21$$
=> $$x=\frac{21}{3}=7$$ years
Thus, her husband's present age =$$4\times7=28$$ years
5 years from now, let her husband's age = $$3z$$ years and her son's age = $$z$$ years
Her husband's age 5 years from now = $$28+5=33$$ years
=> $$3z=33$$
=> $$z=\frac{33}{3}=11$$
$$\therefore$$ Son's present age = $$z-5=11-5=6$$ years
=> Ans - (C)
Present ages of A and B are in ratio 3 : 5. 7 years later B's age will be twice the age of C. If C celebrated his 10 th birthday 4 years ago, then what is the present age (in years) of A?
C celebrated his 10th birthday 4 years ago, => C's present age = $$10+4=14$$ years
Also, B's age after 7 years = $$2\times(14+7)=2\times21=42$$ years
=> B's present age = $$42-7=35$$ years
$$\therefore$$ A's present age = $$\frac{3}{5}\times35=3\times7=21$$ years
=> Ans - (B)
Ratio of present ages of A and B is 4 : 5. After 5 years age of B will be 35 years. What is the present age (in years) of A?
Let A's present age = $$4x$$ years and B's present age = $$5x$$ years -----------(i)
Age of B after 5 years = 35 years
=> B's present age = $$35-5=30$$ years
From equations (i) and (ii), => $$5x=30$$
=> $$x=\frac{30}{5}=6$$
$$\therefore$$ A's present age = $$4\times6=24$$ years
=> Ans - (A)
The present ages of two persons are 36 and 50 years respectively if after n years the ratio of their ages will be 3:4 then the value of n is
Present ages of the persons are 36 and 50 years respectively.
According to ques,
=> $$\frac{36+n}{50+n}=\frac{3}{4}$$
=> $$144+4n=150+3n$$
=> $$4n-3n=150-144$$
=> $$n=6$$
=> Ans - (D)
The ratio of the ages of A, B and C is 5 : 8 : 9. If the sum of the ages of A and C is 56 years, the age of B will be
Let the ages of A, B and C respectively be $$5x,8x$$ and $$9x$$ years.
According to ques, => $$5x+9x=56$$
=> $$x=\frac{56}{14}=4$$
$$\therefore$$ B's age = $$8\times4=32$$ years
=> Ans - (D)
5 year hence, ratio of ages of A and B will be 7 : 5 and difference between their ages will be 4 years. What are present ages (in years) of A and B respectively?
Let ages of A and B five years later be $$7x$$ and $$5x$$ years respectively.
According to ques, => $$7x-5x=4$$
=> $$x=\frac{4}{2}=2$$
Thus, A's present age = $$7(2)-5=9$$ years
B's present age = $$5(2)-5=5$$ years
=> Ans - (C)
The ratio of present ages of Anil and Aakash is 4 : 5. Three years later their ages will be in ratio 7 : 8. What is the present age (in years) of Anil?
Let present ages of Anil and Aakash be $$4x$$ and $$5x$$ years respectively.
According to ques, 3 years later
=> $$\frac{4x+3}{5x+3}=\frac{7}{8}$$
=> $$32x+24=35x+21$$
=> $$35x-32x=24-21$$
=> $$3x=3$$
=> $$x=1$$
$$\therefore$$ Present age of Anil = $$4\times1=4$$ years
=> Ans - (C)
The ratio of present ages of L and N is 7 : 5. If the age of N after seven years will be 32 years, then what is the present age (in years) of L?
Let present ages of L and N be $$7x$$ years and $$5x$$ years respectively.
Thus, N's age after 7 years = $$5x+7=32$$
=> $$5x=32-7=25$$
=> $$x=\frac{25}{5}=5$$
$$\therefore$$ L's age = $$7\times5=35$$ years
=> Ans - (B)
The ratio of present ages of P and Q is 5 : 8. Three years later their ages will be in ratio 8 : 11. What is the present age (in years) of Q?
Let present ages of P and Q be $$5x$$ and $$8x$$ years respectively.
According to ques, 3 years later
=> $$\frac{5x+3}{8x+3}=\frac{8}{11}$$
=> $$55x+33=64x+24$$
=> $$64x-55x=33-24$$
=> $$9x=9$$
=> $$x=1$$
$$\therefore$$ Present age of Q = $$8\times1=8$$ years
=> Ans - (D)
The ratio of the present ages of Aman and Ankit is 2 : 1 and the sum of their present ages is 72 years. What will be the Aman's age (in years) after 6 years?
Let present ages of Aman and Ankit be $$2x$$ years and $$x$$ years respectively.
=> Sum of ages = $$2x+x=3x=72$$
=> $$x=\frac{72}{3}=24$$
Thus, Aman's age after 6 years = $$2(24)+6$$
= $$48+6=54$$ years
=> Ans - (D)
Ratio of present ages of P and Q is 9 : 4. The difference between their ages is 20 years. What will be the sum (in years) of their ages after 10 years?
Let present ages of P and Q be $$9x$$ and $$4x$$ years respectively.
According to ques, => $$9x-4x=5x=20$$
=> $$x=\frac{20}{5}=4$$
$$\therefore$$ Sum (in years) of their ages after 10 years = $$(9x+10)+(4x+10)$$
= $$13(4)+20=52+20=72$$
=> Ans - (C)
Seven years ago, the age of Sahil was equal to the present age of Nihal. Sum of Sahil's age 5 year ago and Nihal's age 6 years later is 58 years. If Ruchi is 4 years elder to Sahil, then what will be Ruchi's age (in years) after 10 years?
Let present ages of Sahil and Nihal be $$s$$ years and $$n$$ years respectively.
According to ques, => $$s-7=n$$ ----------(i)
Also, $$(s-5)+(n+6)=58$$
=> $$s+n=58-1=57$$
Substituting value from equation (i), we get :
=> $$s+s-7=57$$
=> $$2s=57+7=64$$
=> $$s=\frac{64}{2}=32$$
Thus, Ruchi's age = $$32+4=36$$ years
$$\therefore$$ Ruchi's age (in years) after 10 years = $$36+10=46$$ years
=> Ans - (B)
A and B have to type a book together containing 120 pages. A takes 9 hrs to type 36 pages and B takes 5 hrs to type 40 pages. A typed first 60 pages alone and the last 60 pages were typed by A and B together. How much time (in hours) will be taken to type the complete book?
A takes 9 hrs to type 36 pages
=> A's efficiency = $$\frac{36}{9}=4$$ pages/hr
Similarly, B's efficiency = $$\frac{40}{5}=8$$ pages/hr
A typed first 60 pages alone, => Time taken to print 60 pages = $$\frac{60}{4}=15$$ hours
Similarly, time taken to print last 60 pages by A and B together = $$\frac{60}{(4+8)}=5$$ hours
$$\therefore$$ Total time taken to complete the book = $$15+5=20$$ hours
=> Ans - (B)
Anil is as much younger to Vivek as he is older to Tarun. If the total of the ages of Vivek and Tarun is 48 years, how old is Anil?
Let Anil's age = $$x$$ years
Let Anil is $$n$$ years elder than Tarun and $$n$$ years younger than Vivek.
=> Tarun's age = $$(x-n)$$ years
and Vivek's age = $$(x+n)$$ years
Sum of ages of Vivek and Tarun = $$(x-n)+(x+n)=48$$
=> $$2x=48$$
=> $$x=\frac{48}{2}=24$$ years
=> Ans - (C)
The sum of ages of 4 children born at intervals of 4 years each is 60. What is the age of the youngest child?
Let ages of the 4 children be $$(x),(x+4),(x+8),(x+12)$$ years
Sum of ages = $$(x)+(x+4)+(x+8)+(x+12)=60$$
=> $$4x+24=60$$
=> $$4x=60-24=36$$
=> $$x=\frac{36}{4}=9$$
$$\therefore$$ Age of youngest child = $$x=9$$ years
=> Ans - (B)
The ratio of the ages of man and his wife is 4:3. After 4 years, the ration will be 9:7. If at the time of marriage, the ratio was 5:3, how many years ago were they married?
Let the present age of man = $$4x$$ years and wife = $$3x$$ years
According to ques,
=> $$\frac{4x+4}{3x+4}=\frac{9}{7}$$
=> $$28x+28=27x+36$$
=> $$28x-27x=36-28$$
=> $$x=8$$
Thus, man's age = $$4\times8=32$$ years and his wife's age = $$24$$ years
Let they were married $$x$$ years ago, then ratio at the time of marriage = 5 : 3
=> $$\frac{32-x}{24-x}=\frac{5}{3}$$
=> $$96-3x=120-5x$$
=> $$5x-3x=120-96$$
=> $$2x=24$$
=> $$x=\frac{24}{2}=12$$ years
=> Ans - (A)
X is four years older than Y who is twice as old as Z. If the total ages of X, Y and Z be 34, how old is X?
Let Z's age = $$m$$ years
=> Y's age = $$2m$$ years
and X's age = $$(2m+4)$$ years
Sum of ages of X,Y and Z = $$(2m+4)+2m+m=34$$
=> $$5m+4=34$$
=> $$5m=34-4=30$$
=> $$m=\frac{30}{5}=6$$
$$\therefore$$ X's age = $$2(6)+4=16$$ years
=> Ans - (D)
Mrs. Lata was 3 times as old as her son 8 years ago. Their total age is 64 years now. How old (in years) is Mrs. Lata now?
Let Mrs. Lata's age = $$x$$ years
=> Son's age = $$(64-x)$$ years
According to ques,
=> $$3(64-x-8)=(x-8)$$
=> $$3(56-x)=x-8$$
=> $$168-3x=x-8$$
=> $$3x+x=168+8$$
=> $$4x=176$$
=> $$x=\frac{176}{4}=44$$ years
=> Ans - (D)
Mahesh is ’60’ years old. Ram is ‘5’ years junior to Mahesh and ‘4’ years senior to Raju. The youngest brother of Raju is Babu and he is ‘6’ years junior to him. What is the age difference between Mahesh and Babu ?
Mahesh's age = 60 years
=> Ram's age = $$60-5=55$$ years
and Raju's age = $$55-4=51$$ years
=> Babu's age = $$51-6=45$$ years
$$\therefore$$ Age difference between Mahesh and Babu = $$60-45=15$$ years
=> Ans - (B)
The age of Ram is double as that of Shyam and half as that of Suresh. If the sum of their ages is 70, what is the age of Ram ?
Let Shyam's age = $$x$$ years
=> Ram's age = $$2x$$ years
and Suresh's age = $$4x$$ years
Thus, sum of ages = $$x+2x+4x=70$$
=> $$7x=70$$
=> $$x=\frac{70}{7}=10$$ years
$$\therefore$$ Ram's age = $$2\times10=20$$ years
=> Ans - (A)
The average age of father and his son is 22 years. The ratio of their ages is 10 : 1 respectively. What is the age of the son ?
Let son's age = $$x$$ years
=> Father's age = $$10x$$ years
Average age = $$\frac{x+10x}{2}=22$$
=> $$11x=22\times2=44$$
=> $$x=\frac{44}{11}=4$$ years
=> Ans - (B)
Veni is an year older than Smith. Smith is two years older than Salim. Raju is an year older than Salim. Who is the youngest of all ?
Let Smith's age = 10 years
=> Veni's age = 10 + 1 = 11 years
Salim's age = 10 - 2 = 8 years
=> Raju's age = 8 + 1 = 9 years
Clearly, from above equations, Salim is the youngest of all.
=> Ans - (B)
Ronald and Elan are working on an Assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take working together on two different computers to type an assignment of 110 pages ?
Ronald takes 6 hours to type 32 pages
no.of pages typed by ronald per hour = 32/6 = 16/3
Elan takes 5 hours to type 40 pages
no.of pages typed by elan per hour = 40/5 = 8
in 1hr, both can type 8+16/3 pages = 40/3
time taken by both to type 110 pages = 110/(40/3) = 33/4 = 8hrs 15mins ( $$\because$$ 1/4 hr = 15mins)
so the answer is option C.
An employer reduces the number of employees in the ratio 8 : 5 and increases their wages in the ratio 7 : 9. As a result, the overall wages bill is
Let's say employees were change from 8x to 5x and wage per employee is changed from 7y to 9y
Hence total wage is changed from 56xy to 45xy or in a ratio of 56:45
The average age of a jury of 5 is 40. If a member aged 35 resigns and man aged 25 becomes a member, then the average age of the new jury is
Initially, sum of ages of the jury = 200,
then man aged 35 resigns, sum of ages = 200-35
then man aged 25 joins, sum of ages = 200-35+25
Final number of members in the jury =5
So, average age of the jury = (200-35+25)/5 = 38
A boy’s age is one fourth of his father’s age. The sum of the boy’s age and his father’s age is 35. What will be father’s age after 8 years ?
Let father's age = $$4x$$ years
=> Son's age = $$\frac{1}{4}\times4x=x$$ years
Thus, sum of their ages = $$4x+x=35$$
=> $$x=\frac{35}{5}=7$$
$$\therefore$$ Father's age after 8 years = $$4(7)+8=36$$ years
=> Ans - (D)
I am three times as old as my son. 15 years hence, I will by twice as old as my son. The sum of our ages is
Let's say son's age is $$x$$
hence father's present age will be $$3x$$
after 15 years son's age will be $$x+15$$ and father's age will be $$3x+15$$ and it is twice the age of son
so $$3x+15$$ = 2 ($$x+15$$)
solve for $$x$$
At present, the ratio of the ages of Maya and Chhaya is 6:5 and fifteen years from now, the ratio will get changed to 9:8. Maya's present age is
Let's say maya's age is $$6x$$ and chaya's age is $$5x$$.
after 15 years ages will be $$6x+15$$ and $$5x+15$$.
New ratio will be $$\frac{6x+15}{5x+15} = \frac{9}{8}$$.
After solving above equation we will get $$x$$ equals to 5
So maya's age will be 30.
The ratio of the ages of Ram and Rahim 10 years ago was 1 : 3. The ratio of their ages five years hence will be 2 : 3. Then the ratio of their present ages is
Let present ages of Ram and Rahim be $$x$$ and $$y$$ years respectively.
According to ques, ratio of their ages 10 years ago is :
=> $$\frac{x-10}{y-10}=\frac{1}{3}$$
=> $$3x-30=y-10$$
=> $$3x-y=20$$ ------------(i)
Also, five years hence, => $$\frac{x+5}{y+5}=\frac{2}{3}$$
=> $$3x+15=2y+10$$
=> $$2y-3x=5$$ -----------(ii)
Adding equation (i) and (ii),
=> $$y=20+5=25$$
Substituting it in equation (i), we get :
=> $$3x=20+25=45$$
=> $$x=\frac{45}{3}=15$$
$$\therefore$$ Ratio of Ram and Rahim's ages = $$\frac{15}{25}=\frac{3}{5}$$
=> Ans - (B)
In a family, mother’s age is twice that of daughter’s age. Father is 10 years older than mother. Brother is 20 years younger than his mother and 5 years older than his sister. What is the age of the father ?
Let daughter's age = $$x$$ years
=> Mother's age = $$2x$$ years
Thus, father's age = $$(2x+10)$$ years
=> Brother's age = $$(2x-20)$$ years ------------(i)
Also, brother's age = $$(x+5)$$ years ----------(ii)
From equation (i) and (ii),
=> $$2x-20=x+5$$
=> $$2x-x=20+5$$
=> $$x=25$$
$$\therefore$$ Father's age = $$2(25)+10=60$$ years
=> Ans - (B)
Ravi has spent a quarter (1/4) of his life as a boy, one-fifth (1/5) as a youth, one-third (1/3) as man and thirteen (13) years in old age. What is his present age?
Let present age = $$x$$ years
Life spent as a boy = $$\frac{x}{4}$$ years
Similarly, life spent as youth = $$\frac{x}{5}$$ years
According to ques,
=> $$\frac{x}{4}+\frac{x}{5}+\frac{x}{3}+13=x$$
=> $$\frac{15x+12x+20x}{60}+13=x$$
=> $$\frac{47x+780}{60}=x$$
=> $$47x+780=60x$$
=> $$60x-47x=780$$
=> $$x=\frac{780}{13}=60$$ years
=> Ans - (C)
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