The ratio of the sum and difference of the ages of the father and the son is 11 : 3. Consider the following statements: 1. The ratio of their ages is 8 : 5. 2. The ratio of their ages after the son attains twice the present age will be 11 : 8. Which of the statements given above is/are correct?

Question

The ratio of the sum and difference of the ages of the father and the son is 11 : 3. Consider the following statements: 1. The ratio of their ages is 8 : 5. 2. The ratio of their ages after the son attains twice the present age will be 11 : 8. Which of the statements given above is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

LohaHridoy

5 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 2 : 2 only

Calculation:

Let the ages of the father & son be ‘x’ years and ‘y’ years

respecthe tively

So, ratio of the sum & difference between their ages

⇒ (x + y)/(x – y) = 11/3

⇒ 3x + 3y = 11x – 11y

⇒ 8x = 14y

⇒ x/y = 7/4 ----(1)

⇒ Ratio of their current ages = 7 ∶ 4

Clearly, Statement 1 is incorrect.

Now, a son will attain twice his present age after ‘y’ years.

The father and son's ages after y year are (x + y) & (y + y)

Hence, the ratio of father and son's present age

⇒ Ratio of their ages after ‘y’ years = (x + y)/(y + y)

⇒ (x/2y) + (y/2y)

⇒ (1/2)

From equation (1)

⇒(1/2) = 11/8

⇒ (x + y)/(2y) = 11/8

Therefore, Statement 2 is correct

∴ Only statement 2 is correct