Ratio and Proportion: Aptitude Questions with Answers

Review Ratio and Proportion Concepts

Q. 1 Simplify the ratio: 6 : 9

A) 3 : 5

B) 2 : 5

C) 2 : 3

D) 3 : 4

Check Solution

Ans: C

Divide both the numbers by 3

Q. 2 If the ratio of Anjana’s income to Baani’s income is 5:4 and the ratio of their expenditures is 3:2. If Anjana saves $2000 and Baani saves $1000, what’s the ratio of their savings respectively?

A) 5:4

B) 4:5

C) 3:2

D) 2:1

Check Solution

Ans: A) 5:4.

Let A’s income and B’s income be 5x and 4x , and their expenditures be 3y and 2y .
Savings = Income – Expenditure.
For A: 5x−3y=2000 , For B: 4x−2y=1000 .
Solving these, x=1000 , y=1000 .
Thus, 5x:4x=5:4.

Q. 3 Two numbers are in the ratio 3:5. When you subtract 9 from each, the ratio magically changes to 12:23. What are these numbers?

A) 45, 75

B) 36, 60

C) 33, 55

D) 54, 90

Check Solution

Ans: C) 33, 55.

Let the numbers be 3x and 5x.
After subtracting 9, $\frac{3x – 9}{5x – 9} = \frac{12}{23}$.
Cross-multiplying, 23(3x−9)=12(5x−9).
$69x – 207 = 60x – 108 \Rightarrow 9x = 99 \Rightarrow x = 11$.
The numbers are $3 \times 11 = 33$ and $5 \times 11 = 55$.

Q. 4 The ratio of two numbers is 3:5. Add 10 to each, and the new ratio changes to 5:7. Find the original numbers?

A) 15 and 25

B) 21 and 35

C) 18 and 30

D) 24 and 40

Check Solution

Ans: A) 15 and 25.

Let the numbers be 3x and 5x.
After increasing by 10, $\frac{3x + 10}{5x + 10} = \frac{5}{7}$.
Cross-multiplying, 7(3x+10)=5(5x+10) .
Expanding and solving, 21x+70=25x+50, so $4x = 20 \Rightarrow x = 5$.
Thus, the numbers are $3 \times 5 = 15$ and $5 \times 5 = 25$.

Q. 5 If Arya’s salary compared to Bhuvi’s salary is like 4 to 7. After a $4000 raise for both, their salary ratio shifts to 6:11. What was Arya’s original salary?

A) $16000

B) $12000

C) $10000

D) $14000

Check Solution

Ans: D) $14000.

Let A’s and B’s original salaries be 4x and 7x.
After the increase, $\frac{4x + 4000}{7x + 4000} = \frac{6}{11}$​.
Cross-multiplying, 11(4x+4000)=6(7x+4000).
Expanding, 44x+44000=42x+24000, so $2x = 20000 \Rightarrow x = 10000$.
A’s original salary = $4 \times 10000 = 40000$.

A quick reference table can simplify solving tricky ratio problems.

Q. 6 Three numbers are in 2:3:5 ratio. Interestingly, the sum of the first and third exceeds the second by 16. Can you decode the numbers?

A) 8, 12, 20

B) 4, 6, 10

C) 12, 18, 30

D) 6, 9, 15

Check Solution

Ans: A) 8, 12, 20.

Let the numbers be 2x , 3x , and 5x .
According to the problem, $2x + 5x – 3x = 16 \Rightarrow 4x = 16 \Rightarrow x = 4$.
So, the numbers are $2 \times 4 = 8$, $3 \times 4 = 12$, and $5 \times 4 = 20$.

Q. 7 A bag of colorful balls contains red, blue, and green balls in a 3:4:5 ratio. If there are 60 green balls, how many balls are in the bag altogether?

A) 120

B) 144

C) 180

D) 150

Check Solution

Ans: B) 144.

Let the numbers of red, blue, and green balls be 3x, 4x, and 5x, respectively.
Since 5x=60, x=12.
Total number of balls = $3x + 4x + 5x = 12x = 12 \times 12 = 144$.

Q. 8 The incomes of A, B, and C are in the ratio 7:9:12, while their expenses are in the ratio 8:9:15. If their respective savings are $200, $150, and $300, what’s A’s income?

A) $1400

B) $2100

C) $2800

D) $3500

Check Solution

Ans: A) $1400.

Let A’s, B’s, and C’s incomes be 7x, 9x, and 12x, and their expenses be 8y, 9y, and 15y.
Since income – expense = savings, we get:
7x−8y=200, 9x−9y=150, and 12x−15y=300.
Solving these, we find x=200.
So, A’s income = $7 \times 200 = 1400$.

Q. 9 A and B’s present ages are tied at a ratio of 4:5. But if you rewind five years, their ages were in the ratio 3:4. Can you determine their present ages?

A) 20 and 25 years

B) 16 and 20 years

C) 24 and 30 years

D) 28 and 35 years

Check Solution

Ans: A) 20 and 25 years.

Let A’s age and B’s age be 4x and 5x respectively.
Five years ago, $\frac{4x – 5}{5x – 5} = \frac{3}{4}$​.
Cross-multiplying, 4(4x−5)=3(5x−5).
This gives 16x−20=15x−15, so x=5.
Thus, A’s age = $4 \times 5 = 20$, B’s age = $5 \times 5 = 25$.

Q. 10 Two trains race with speed ratios of 5:8. The faster train covers 400 km in just 5 hours. What’s the speed of the slower train?

A) 40 km/hr

B) 50 km/hr

C) 60 km/hr

D) 80 km/hr

Check Solution

Ans: B) 50 km/hr.

Speed of the faster train = $\frac{400}{5} = 80$ km/hr.
Let the speed of the slower train be x. Then, $\frac{x}{80} = \frac{5}{8}$, so $x = 80 \times \frac{5}{8} = 50$ km/hr.

Q. 11 A chocolate manufacturer packs dark, milk, and white chocolates in a box in the ratio 4:5:6. If the manufacturer decides to add 12 more milk chocolates to the box, the new ratio becomes 4:6:6. How many chocolates were initially in the box?

A) 45

B) 180

C) 120

D) 135

Check Solution

Ans: B) 180

Let the total initial number of chocolates be 4x+5x+6x=15x

When 12 milk chocolates are added, the ratio changes: $\frac{4x}{5x+12} = \frac{4}{6}$

Cross-multiplying: 24x = 20x+48  ⟹  4x=48  ⟹  x=12

Initial total chocolates = 15x=15×12=180

Q. 12 A farmer has cows and goats in the ratio 7:9. If 20 more cows are added to the farm, the ratio changes to 4:3. How many goats are currently on the farm?

A) 36

B) 54

C) 63

D) 72

Check Solution

Ans: A) 36

Let the number of cows and goats be 7x and 9x respectively

When 20 more cows are added, the new ratio is: (7x+20)/9x = 4/3

Cross-multiplying: 21x + 60= 36x  ⟹  15x = 60  ⟹  x=4

Number of goats =9×4 = 36

Q. 13 In a town, the ratio of people speaking English, Spanish, and French is 8:6:5. If the total population is 19,000, how many more people speak English than French?

A) 1000

B) 1500

C) 2000

D) 3000

Check Solution

Ans: D) 3000

The total ratio sum is 8+6+5=19

The value of one ratio unit = 19000/19 = 1000

Number of people speaking English = 8×1000 = 8000

Number of people speaking French = 5×1000=5000

Difference = 8000−5000=3000

Q. 14 A jar contains a mixture of juice and water in the ratio 5:3. If 16 litres of the mixture are replaced with water, the new ratio becomes 3:5. What is the initial volume of the mixture?

A) 24 litres

B) 32 litres

C) 40 litres

D) 48 litres

Check Solution

Ans: C) 40 litres

Let the initial volume of the mixture be 5x + 3x = 8x

When 16 litres are replaced, the juice and water volumes change:

Juice: 5x − 5/8×16

Water: 3x+16 − 3/8×16 = 3x + 10

The new ratio is: $\frac{5x – 10}{3x + 16 – 6} = \frac{3}{5}$

Cross-multiplying: $5*(5x−10) = 3*(3x+10) ⟹ 16x = 80 ⟹ x = 5$

Initial volume = 8x = 8×5 = 40

Q. 15 Simplify the ratio: 2 : 4

A) 1 : 2

B) 1 : 3

C) 2 : 3

D) 2 : 5

Check Solution

Ans: A

Divide both the numbers by 2

Q. 16 There are 60 Dogs and 180 Cats . Find ratio of Dogs to Cats

A) 2 : 3

B) 1 : 3

C) 2 : 5

D) 3 : 5

Check Solution

Ans: B

Divide both the numbers by 60

Q. 17 In a mixture of 44 units, Shampoo is 20 units. Find the in the ratio of Shampoo to Water in the mixture.


A)

5 : 6

B)

7 : 9

C)

6 : 5

D)

3 : 4

Check Solution

Ans: A

Since Shampoo = 20. Water = 44 – 20 = 24.

Simplify ratio 20 : 24 by dividing it by 4 to get 5 : 6

Q. 18 Amanda got a financial aid package totaling \$8000, split between loans and grants. She allocated one-quarter of the loan amount and three-fifths of the grant amount for her personal living expenses, which came to \$2875. How much of the financial aid did Amanda receive as loans?

A) 6000

B) 5500

C) 3500

D) 2500

Check Solution

Ans: B

L + G = 8000

L/4 + 3G/5 = 2875

L + 12G/5 = 11500

7G/5 = 3500

G = 2500

L = 8000-2500 = 5500

Next Topic: Aptitude Questions for Profit and Loss

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