Ratio and Proportion

Question 1

Present age of Vinod and Ashok are in ratio of 3:4 respectively. After 5 years, the ratio of their ages becomes 7:9 respectively. What is Ashok’s present age is ?

• A. 40 years
• B. 28 years
• C. 32 years
• D. 36 years

Answer: (A)

Let the present age of Vinod and Ashok be 3x years and 4x years respectively.

Then (3x+5) / (4x+5)  = 7 / 9 

∴ 9(3x + 5) = 7(4x + 5)
∴ 27x + 45 = 28x + 35
∴ x = 10
∴ Ashok’s present age = 4x = 40 years 

Question 2

At present, the ratio between ages of Ram and Shyam is 6:5 respectively. After 7 years, Shyam’s age will be 32 years. What is the present age of Ram?

• A. 32
• B. 40
• C. 30
• D. 36

Answer: (C)

Let the present age of Ram and Shyam be 6x years and 5x years respectively.

Then 5x + 7 = 32
∴      5x = 25
∴        x = 5
∴ Present age of Ram = 6x = 30 years

Question 3

The present ages of A, B and C are in proportions 4:5:9. Nine years ago, sum of their ages was 45 years. Find their present ages in years

• A. 15,20,35
• B. 20,24,36
• C. 20,25,45
• D. 16,20,36

Answer: (D)

Let the current ages of A, B and C be ax years, 5x years and 9x respectively.

Then (4x-9) + (5x-9) + (9x-9) =45
∴ 18x – 27 = 45
∴ 18x = 72
∴ x = 4

Present ages of A, B and C are 4x = 16, 5x = 20, 9x = 36 respectively.

Question 4

Two numbers are in the ratio of 2:9. If their H. C. F. is 19, numbers are:

• A. 6, 27
• B. 8, 36
• C. 38, 171
• D. 20, 90

Answer: (C)

Let the numbers be 2X and 9X
Then their H.C.F. is X, so X = 19
∴ Numbers are (2x19 and 9x19) i.e. 38 and 171

Question 5

In a box, there are 10p, 25p and 50p coins in the ratio 4:9:5 with the total sum of Rs 206. How many coins of each kind does the box have?

• A. 200, 360, 160
• B. 135, 250, 150
• C. 90, 60, 110
• D. Cannot be determined

Answer: (A)

Let the number of 10p, 25p, 50p coins be 4x, 9x, 5x respectively. Then, 4x/10 + 9x/4 + 5x/2 = 206 (Since, 10p = Rs 0.1, 25p = Rs 0.25, 50p = Rs 0.5) => 8x + 45x + 50x = 4120 (Multiplying both sides by 20 which is the LCM of 10, 4, 2) => 103x = 4120 => x = 40. Therefore, No. of 10p coins = 4 x 40 = 160 (= Rs 16) No. of 25p coins = 9 x 40 = 360 (= Rs 90) No. of 50p coins = 5 x 40 = 200 (= Rs 100)

Question 6

Mark, Steve and Bill get their salaries in the ratio of 2:3:5. If their salaries are incremented by 15%, 10%, and 20% respectively, the new ratio of their salaries becomes:

• A. 8:16:15
• B. 23:33:60
• C. 33:30:20
• D. 21:25:32

Answer: (B)

Let their old salaries be 2a, 3a, 5a respectively. Then, their new salaries become: 115% of 2a = 2a x 1.15 = 2.3a 110% of 3a = 3a x 1.10 = 3.3a 120% of 5a = 5a x 1.20 = 6a So, the new ratio becomes 2.3a:3.3a:6a Upon simplification, this becomes 23:33:60

Question 7

In a library, the ratio of the books on Computer, Physics and Mathematics is 5:7:8. If the collection of books is increased respectively by 40%, 50% and 75%, find out the new ratio:

• A. 3:9:5
• B. 7:5:3
• C. 2:3:4
• D. 2:5:4

Answer: (C)

40% increase will lead to a factor of 140 and similarly 150 and 175 so new ratio is (5*140):(7*150):(8*175) on solving we get 2:3:4

Question 8

The ratio 5:3 represents 16 liters of a mixture containing milk and water. If 4 liters of water is added and 4 liters of milk is extracted from the mixture, then the ratio of the mixture will be:

• A. 7:3
• B. 5:6
• C. 2:3
• D. None of these

Answer: (D)

Amount of Milk in 16 litres of mixture: (5/8) x 16 = 10 litres Amount of Water in 16 litres of mixture: 16-10 = 6 litres If we add 4 litres of water and extract 4 litres of milk, the total volume remains the same. Amount of Milk in 16 litres of new mixture: = 10 - 4 = 6 litres Amount of Water in 16 litres of new mixture: = 6 + 4 = 10 litres So, the new ratio becomes 3:5.

Question 9

If the ages of Jacob, Max and Samuel are in the proportion 3:5:7 and the average of their ages is 25 years, then find the age of the youngest person.

• A. 15 years
• B. 10 years
• C. 7 years
• D. 18 years

Answer: (A)

Let their ages be 3a, 5a and 7a. Then, (3a + 5a + 7a) / 3 = 25 => 15a/3 = 25 => 5a = 25 => a = 5 Therefore, age of the youngest person = 3a = 15 years

Question 10

The ratio of the speed of two trains is 7:8. If the second train covers 400 km in 4 h, find out the speed of the first train.

• A. 69.4 km/h
• B. 78.6 km/h
• C. 87.5 km/h
• D. 40.5 km/h

Answer: (C)

Let the speed of the two trains be 7x and 8x. Then, 8x = 400 / 4 ⇒ 8x = 100 ⇒ x = 12.5 km/h. Hence, speed of the first train = 7x = 7 × 12.5 = 87.5 km/h.