Solved Questions on Ratio and Proportion
1. The ratio of boys and girls in a college is 7 : 8. If the percentage increase in the number of boys and girls is 20% and 10% respectively, what will be the new ratio?
a) 8 : 9
b) 17 : 18
c) 21 : 22
d) 24 : 33
Answer: c) 21 : 22
Explanation: Let the no. of boys = 7x
The no. of girls = 8x
20% increase in boys strength = [20/100] x 7x = 7x/5
The number of boys = 7x + 7x/5= 42x/5
10% increase in girls = [10/100] x 8x
= 4x/5
The number of girls = 8x + 4x/5 = 44x/5
42x/5 : 44x/5 = 42x : 44x
42 : 44 = 21 : 22
2. If the ratio of men to women in a company is 3 : 5, how many men are there in a company with a total of 160 employees?
a) 90
b) 60
c) 75
d) 45
Answer: b) 60
Explanation: Ratio of men to women = 3 : 5
Men in the company = (3/(3 + 5)) x 160 = 60 men.
3. The sum of three numbers is 98. If the ratio of the first to second is 2 : 3 and that of the second to the third is 5 : 8, then the second number is:
a) 20
b) 30
c) 48
d) 58
Answer: b) 30
Explanation: Let the three numbers be A, B, and C respectively.
A : B = 2 : 3 ---> (1)
B : C = 5 : 8 -----> (2)
Multiplying (1) by 5 and (2) by 3,
A : B = 10 : 15
B : C = 15 : 24
A : B : C = 10 : 15 : 24
Sum of ratio = 10 + 15 + 24 = 49
B = (15/49) × 98 = 30
4. Salaries of Robert and Sam are in the ratio 2 : 3. If the salary of each is increased by $4000, the new ratio becomes 40 : 57. What is Sam's salary?
a) $17000
b) $20000
c) $25500
d) $38000
Answer: d) $38000
Explanation: Let the original salaries of Robert and Sam be $2x and $3x respectively.
Then, ( 2x + 4000) / (3x + 4000) = 40/57
= 57(2x + 4000) = 40(3x + 4000)
= 6x = 68,000
= 3x = 34,000
Sam’s present salary = (3x + 4000) = $(34000 + 4000) = $38,000.
5. If the ratio of a to b is 3 : 4 and the value of a is 12, what is the value of b?
a) 16
b) 9
c) 15
d) 18
Answer: a) 16
Explanation: a : b = 3 : 4
¾ = 12/b
3b = 48
b = 48/3 = 16
Practice Questions on Ratio and Proportion
1. In a school, the ratio of students to teachers is 25 : 2. If there are 400 students, how many teachers are there?
a) 25
b) 28
c) 30
d) 32
Answer: d) 32
2. If (a + b) : (b + c) : (c + a) = 6 : 7 : 8 and (a + b + c) = 14, Find the value of c.
a) 3
b) 4
c) 5
d) 6
Answer: d) 6
3. If a box that holds twelve mirrors is accidentally dropped, which of the following ratios is not possible for the ratio of broken mirrors to unbroken mirrors?
a) 2 : 3
b) 1 : 2
c) 2 : 5
d) 4 : 1
Answer: a) 2 : 3
4. If the ratio of boys to girls in a classroom is 2 : 3 and there are 15 girls, how many boys are there?
a) 10
b) 12
c) 15
d) 18
Answer: a) 10
5. Three people, A, B and C, shared an amount of $735. If each of them had received $25 less, their shares would have been in the ratio of 1 : 3 : 2. How much money did C receive?
a) $225
b) $245
c) $250
d) $280
Answer: b) $245
6. The ages of A and B are in the ratio 5 : 3. If the sum of their ages is 64 years, how old is A?
a) 10
b) 20
c) 40
d) 60
Answer: c) 40
7. If the ratio of the lengths of two sides of a rectangle is 3 : 7 and the perimeter of the rectangle is 40 cm. Find the area of the rectangle.
a) 20 sq. units
b) 30 sq. units
c) 40 sq. units
d) 84 sq. units
Answer: d) 84 sq. units
8. The ratio of the incomes of A, B and C is 5 : 3 : 7. If their total income is $6,000, what is C's income?
a) $2000
b) $2200
c) $2500
d) $2800
Answer: d) $2800
10. The ages of three boys are in the ratio of 3 : 5 : 7 and their average age is 25 years. What is the age of the youngest boy?
a) 8 years
b) 10 years
c) 12 years
d) 15 years
Answer: d) 15 years
