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The ratio of present ages of Avik and Suman is 2 ∶ 3. 4 years ago, the ratio of ages of Kamal and Avik was 6 ∶ 5, while ratio of ages of Suman and Kamal was 4 ∶ 3. What is the present age of Kamal?

The ratio of present ages of Avik and Suman is 2 ∶ 3. 4 years ago, the ratio of ages of Kamal and Avik was 6 ∶ 5, while ratio of ages of Suman and Kamal was 4 ∶ 3. What is the present age of Kamal? Correct Answer 28

Given:

Avik : Suman = 2 ∶ 3

4 years ago, Kamal : Avik = 6 ∶ 5

Suman : Kamal = 4 ∶ 3

Concept used:

We will be using the concept of ratio.

Calculation:

Let present age of Avik be 2x

Present age of Suman be 3x

Present age of Kamal be y

According to the question,

⇒ (y – 4)/(2x – 4) = 6/5

⇒ 12x – 24 = 5y – 20

⇒ 12x – 5y = 4     ----(1)

According to the question,

⇒ (3x – 4)/(y – 4) = 4/3

⇒ 9x – 12 = 4y – 16

⇒ 9x – 4y = - 4     ----(2)

Add (1) and (2) we get,

⇒ 21x - 9y = 0

⇒ x/y = 9/21

⇒ x/y = 3/7

Kamal = 7 × 4 = 28

∴ The present age of Kamal = 28 years

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