Ratio and Proportion Questions for TISSNET
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Question 1: Five eighth of a number is equal to 60% of another number. What is the ratio between the first number and the second number respectively ?
a) 13:12
b) 12:13
c) 25:24
d) 24:25
e) None of these
1) Answer (D)
Solution:
Let the two numbers be X and Y.
So, $\frac{5}{8}*X = 60 \% Y$
Or, $\frac{5}{8}*X = \frac{3}{5}*Y$
So, $\frac{X}{Y} = \frac{24}{25}$
Hence, the required ratio is 24:25
Question 2: Salaries of A, B and C are in the ratio 2 : 3 : 5. If their salaries were increased by 15%, 10% and 20% respectively, what will be the new ratio of their salaries ?
a) 3: 3: 10
b) 23: 33: 60
c) 10: 11: 20
d) Can’t be determined
e) None of these
2) Answer (B)
Solution:
Let the salaries of A, B and C be 2S,3S and 5S.
If salary of A is increased by 15%, the salary becomes 2S*115% = 2.3S
If salary of B is increased by 10%, the salary becomes 3S*110% = 3.3S
If salary of C is increased by 20%, the salary becomes 5S*120% = 6S
Hence, the new ratio of their salaries becomes 2.3:3.3:6 = 23:33:60
Question 3: Ratio of the earnings of A and B is 4 : 7. If the earnings of A increase by 50% and the earnings of B decrease by 25% the new ratio of their earnings becomes 8 : 7. What are A’s earnings ?
a) Rs. 26, 000
b) Rs. 28, 000
c) Rs. 21, 000
d) Data inadequate
e) None of these
3) Answer (D)
Solution:
Let the earnings of A and B be 4X and 7X respectively.
If earnings of A increase by 50%, he earns 4X*150% = 6X
If earnings of B decrease by 50%, he earns 7X*75% = 21/4X
So, the new ratio becomes 6X:21/4X = 8:7
This information doesn’t give any new information about the value of X and hence it’s value can’t be determined.
Question 4: The number of students studying in College A and B are in the ratio of 3:4. If 50 more students join College A and there is no change in the number of students in College B the ratio becomes 5:6 What is the number of students in College B ?
a) 450
b) 500
c) 400
d) 600
e) None of these
4) Answer (D)
Solution:
Let the number of students in college A and B be 3s and 4s respectively.
If 50 more students join college A, it will have 3s+50 students and the ratio with respect to college B will be 3s+50:4s
This ratio is equal to 5:6
Hence, $\frac{3s+50}{4s}=\frac{5}{6}$
Therefore, $18s+300 = 20s$ or $s=150$
Therefore, the number of students in college B equals $4s=600$
Question 5: Four-seventh of a number is equal to 40% of another number. What is the ratio between the first number and the second number respectively ?
a) 5:4
b) 4:5
c) 10:7
d) 7:10
e) None of these
5) Answer (D)
Solution:
Let the two numbers be X and Y respectively.
So, $\frac{4}{7}*X = 40 \% *Y$
So, $\frac{4}{7}*X = \frac{4}{10} * Y$
Therefore, X:Y = 7:10
Question 6: Populations of two villages X and Y are in the ratio of 5:7 respectively.If the population of village Y increases by 25000 and the population of village X remains unchanged the respective ratio of their populations becomes 25:36 What is the population of village X ?
a) 6,25,000
b) 6,75,000
c) 8,75,000
d) 9,00,000
e) None of these
6) Answer (A)
Solution:
As the ratio of populations of the two villages are in the ratio 5:7, let the respective populations be 5p and 7p
If the population of Y increases by 25000, the population of Y is 7p+25000 and the new ratio equals 5p:7p+25000
This new ratio is 25:36
Hence, $\frac{5p}{7p+25000}=\frac{25}{36}$
Or, $180p = 175p + 625000$
or $p = 125000$
Therefore, the population of X = 5p = 6,25,000
Question 7: Seats for Maths, Physics and Biology are in the ratio of 5:7:8 respectively. There is a proposal to increase these seats by 40% 50% and 75% respectively. What will be the respective ratio of increased seats ?
a) 2:3:4
b) 6:7:8
c) :6:8:9
d) Cannot be determined
e) None of these
7) Answer (A)
Solution:
Let the original number of seats in Maths, Physics and Biology be 5X, 7X and 8X.
So, the respective increases in seats equals 5X*0.4, 7X*0.5 and 8X*0.75
That is 2X, 3.5X and 6X
Hence, the final number of seats equals 5X+2X,7X+3.5X and 8X+6X = 7X,10.5X,14X
So, the final ratio is 7:10.5:14 = 2:3:4
Question 8: Ratio of earnings of A and B is 8 : 9 respectively. If the earnings of A increased by 50% and the earnings of B decrease by 25%, the new ratio of their earnings becomes 16:9 respectively. What are ‘A’ earnings ?
a) Rs. 37,000
b) Rs. 28,500
c) Rs. 22,000
d) Cannot be determined
e) None of these
8) Answer (D)
Solution:
Let the earnings of A and B be 8k and 9k respectively.
New earnings of A = 150/100 * 8k = 12k
New earnings of B = 3/4 * 9k = 6.75k
So, 12k : 6.75k = 16 : 9
But, from this equation, we cannot determine the value of k.
So, option d) is the correct answer.
Question 9: Ravi is older than Simar by 4 years. Four years from now, the respective ratio between Ravi’s age and Simar’s age will be 9:8. What will be the Ravi’s age 15 years ago? (in years)
a) 19
b) 36
c) 17
d) 25
e) 21
9) Answer (C)
Solution:
Let Ravi’s age be x and Simar’s be y.
x=y+4
After 4 years,
(x+4)/(y+4) = 9/8
8x-9y = 4
After solving we get Ravi’s age be 32 years.
15 years before his age is 32-17=17 years.
Question 10: The respective ratio of two numbers is 16 : 21. If the first number is increased by 30% and the second number is decreased by 20%, what will be the respective ratio of the first and the second number?
a) 32 : 21
b) 26 : 21
c) 25 : 21
d) 20 : 21
e) 22 : 21
10) Answer (B)
Solution:
Let the numerator and denominator be x and y.
(x/y) = (16/21)
Now, if the first number is increased by 30% and the second number is decreased by 20% then the ratio is $\frac{1.3*16}{0.8*21}$
Which equals $\frac{208}{168}$
Which equals $\frac{26}{21}$
Option B is the correct answer.
Question 11: A sum of money is divided among A, B, C, and D in the ratio of 2:3:7:11. If the share of C is Rs 2,755 more than the share of A then what is the total amount of money of B and D together ?
a) Rs 4,408
b) Rs 5,510
c) Rs 6,612
d) Rs 7,714
e) None of these
11) Answer (D)
Solution:
Let x be the total amount of money.
Here, share of C is Rs 2,755 more than the share of A i.e
Share of C – Share of A = 2755
i.e (7x/23) – (2x/23) = 2755
Hence, x= 12,673
Total amount of money with B and D together = (3+11)x/23 = 14x/23 = (14*12673)/23 = 7714
Correct option is D.
Question 12: Profit earned by an organization is distributed among officers and clerks in the ration 5 : 3 respectively. If the number of officers is 45 and the number of clerks 80 and the amount received by each officer is Rs. 25,000/-, what was the total amount of profit earned?
a) Rs. 22 lakhs
b) Rs. 18.25 lakhs
c) Rs. 18 lakhs
d) Rs. 23.25 lakhs
e) None of these
12) Answer (C)
Solution:
Let the amount recieved by each clerk be x
$\frac{45*25000}{80*x} = \frac{5}{3}$
x = 8437.5
Total profit = (8437.5*80)+(25000*45) = 18 lakh
Question 13: Mr. X invested a certain amount in Debt and Equity funds in the ratio of 4 : 5 respectively. At the end of one year, he earned a total divided by 30%on his investment. After one year he reinvested the amount including dividend in the ratio of 6 : 7 in Debt and Equity Funds. If the amount reinvested in Equity Funds was Rs. 94,500/-, what was the original amount invested in Equity Funds?
a) Rs. 75,000
b) Rs. 81,000
c) Rs. 60,000
d) Rs. 65,000
e) None of these
13) Answer (A)
Solution:
Since the amount reinvested is in the ratio 6:7,
the amount reinvested in equity is $\frac{7}{6+7}$ of total amount.
$\frac{7}{13}$ x = 94500
x = 94500*13/7
Since there was a 30% profit on this amount,
Original amount = (94500*13)/(7*1.3) = 135000
Amount invested in equity =$\frac{5}{5+4}*135000$ = 75000
Question 14: At present Anil is 1.5 times Purvi’s age. Eight years hence the respective ratio between Anil and Purvi’s age then will be 25: 18. What is the Purvi’s present age?
a) 50 yr
b) 28 yr
c) 42 yr
d) 36 yr
e) None of these
14) Answer (B)
Solution:
Since Anil’s age is 1.5 times the Purvi’s age,
Purvi’s age = x
Anil’s age = 1.5x
$\frac{1.5x+8}{x+8} = \frac{25}{18}$
(1.5x+8)18 = 25(x+8)
27x+144 = 25x+200
2x = 56
x = 28
Question 15: The respective ratio of A and B is 8:7. If the salary of B increases by 20% and the salary of A increases by 21% the new ratio becomes 96: 97 respectively. What is A’s salary?
a) 22560
b) 21600
c) 20640
d) 23040
e) Cannot be determined
15) Answer (E)
Solution:
As we are not given any absolute figures, a unique value of A’s salary cannot be determined.
Question 16: Rs.73,689 are divided between A and B in the ratio of 4 : 7. What is the difference between thrice the share of A and twice of the share of B?
a) Rs.36,699
b) Rs.46,893
c) Rs.20,097
d) Rs.26,796
e) Rs.13,398
16) Answer (E)
Solution:
Share of A = $\frac{4}{11}$ x 73689 = 26796
Thrice share of A = 80388
Share of B = $\frac{7}{11}$ x 73689 = 46893
Twice the share of B = 93786
Difference = 13398
Question 17: A certain amount was to be distributed among A, B and C in the ratio 2 : 3 : 4 respectively, but was erroneously distributed in the ratio 7 : 2 : 5 respectively. As a result of this, B got Rs.40 Less. What is the amount?
a) Rs.210
b) Rs.270
c) Rs.230
d) Rs.280
e) None of these
17) Answer (A)
Solution:
Let the amount be x
If the amount is divided into 9 parts , each part = $\frac{x}{9}$
B’s supposed amount = 3 x $\frac{x}{9}$ = $\frac{x}{3}$
But B’s actual amount = 2 x $\frac{x}{14}$ = $\frac{x}{7}$
$\frac{x}{3}$ – $\frac{x}{7}$ = 40
x = 210
Question 18: The ratio of the present age of Manisha and Deepali is 5 : X. Manisha is 9 years younger than Parineeta. Parineeta’s age after 9 years will be 33 years. The difference between Deepali’s and Manisha’s age is the same as the present age of Parineeta. What should come in place of X?
a) 23
b) 39
c) 15
d) Cannot be determined
e) None of these
18) Answer (E)
Solution:
Parineeta’s present age = 33 – 9 = 24 yrs.
Manisha’s present age = 24 – 9 = 15yrs
Difference between Manisha and Deepali’s prresent ages = Parineeta’s present age
Deepali’s present age = Parineeta’s present age + Manisha’s present age = 24 + 15 = 39 yrs.
Ratio of the present age of Manisha and Deepali = 15 : 39 = 5 : 13
x = 13
Question 19: Six years ago Jagannath was twice as old as Badri if the ratio of their present age is 9:5 respectively .What is the difference between their present ages?
a) 24
b) 30
c) 50
d) Cannot determined
e) None of these
19) Answer (A)
Solution:
Let present age of Jagannath = $9x$ years
=> Badri’s present age = $5x$ years
According to ques, => $(9x-6)=2 \times (5x-6)$
=> $9x-6=10x-12$
=> $10x-9x=12-6$
=> $x=6$
$\therefore$ Difference between their present ages = $9x-5x=4x$
= $4 \times 6=24$
=> Ans – (A)
Question 20: An amount of Rs 1,25,000 is to be distributed among the Sudhir,Soni,Shakunthala in the respective ratio of 2 : 3 : 5.What will be the difference between Soni’s and Sudhir’s Share?
a) 25000
b) 12500
c) 18750
d) 2500
e) None of these
20) Answer (B)
Solution:
Let amount received by Sudhir,Soni and Shakunthala be $2x,3x$ and $5x$ respectively.
=> Total amount = $(2x+3x+5x)=125,000$
=> $10x=125,000$
=> $x=\frac{125,000}{10}=12500$
$\therefore$ Difference between Soni’s and Sudhir’s Share = $3x-2x=x = Rs.$ $12,500$
=> Ans – (B)
