SSC Ages Questions

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 

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

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

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

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

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

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.

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 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

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

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

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.

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.

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

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  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

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.

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.

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 $$ \times \frac {1}{6} $$ = $$ \frac {5}{6}$$

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 $$ \frac {2}{3}$$

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 

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)

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                                                 

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

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                                               

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.

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 = 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            Suresh
Present Age              3x                    x

After 2 years           3x+2                x+2

Given   3x+2 = 2(x+2)

             3x+2 = 2x+4

Therefore, Ramesh Present Age = 3x

                                                          = 3 x 2

                                                          = 6 years                                                                                                              

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)

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)

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

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.

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.

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) 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

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

$$=$$>         $$\ \frac{12+x\ }{20+x}=\ \frac{\ 5}{7}$$  

     $$84+7x=100+5x$$

                     $$2x=16$$

                       $$x=8$$

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.

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

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

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.

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.

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.

                             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

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.

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 

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.

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.

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.

 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.

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

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)

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)

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)

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

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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 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)

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)

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)

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)

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)

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'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)

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)

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)

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 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.

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

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

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)

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 $$x$$

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.

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)

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)

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)