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The ratio of the present ages of two persons A and B is 4 ∶ 3. If 4 years ago, the ratio of their ages was 2 ∶ 1, what is the present age of A and B (in years) respectively?

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UGC NET Paper 1: Held on 23rd Oct 2022 Shift 1
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  1. 8, 6
  2. 9, 7
  3. 12, 9
  4. 9, 12

Answer (Detailed Solution Below)

Option 1 : 8, 6
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Given:

The ratio of the present ages of two persons A and B is 4 ∶ 3.

If 4 years ago, the ratio of their ages was 2 âˆ¶ 1

Calculation:

Let's assume the present ages of A and B are 4x and 3x, respectively.

4 years ago, the ages of A and B were 4x - 4 and 3x - 4, respectively.

The ratio of their ages 4 years ago was (4x - 4) : (3x - 4) = 2 : 1.

So, we can write the equation:

2 / 1 = (4x - 4) / (3x - 4)

Expanding and simplifying the equation, we get:

2 = 4x - 4 / 3x - 4

Multiplying both sides by 3x - 4, we get:

2 ×  (3x - 4) = 4x - 4

Solving for x, we get:

x = 8.

So, the present age of A is 4x = 4 × 8 = 32 years

The present age of B is 3x = 3 × 8 = 24 years.

A : B = 32 : 24 = 8 : 6

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