Ram is 20 years older than Rahul. 'n' years ago Ram was thrice as old as Rahul. '2n' years from now the ratio of the ages of Ram and Rahul will be 15 : 11. What is the value of 'n'?

Given:

Ram is 20 years older than Rahul.

'n' years ago, Ram was thrice as old as Rahul.

'2n' years from now, the ratio of the ages of Ram and Rahul will be 15:11.

Formula Used:

Let's denote the current age of Ram by R and the current age of Rahul by r.

1) R = r + 20

2) R - n = 3(r - n)

3) \(\frac{R + 2n}{r + 2n} = \frac{15}{11}\)

Calculation:

From equation 1:

R = r + 20

From equation 2:

⇒ R - n = 3(r - n)

⇒ r + 20 - n = 3r - 3n

⇒ 2r - 2n = 20

⇒ r - n = 10

From equation 3:

⇒ \( \frac{R + 2n}{r + 2n} = \frac{15}{11}\)

⇒ 11(R + 2n) = 15(r + 2n)

⇒ 11(r + 20 + 2n) = 15(r + 2n)

⇒ 11r + 220 + 22n = 15r + 30n

⇒ 220 = 4r + 8n

⇒ 55 = r + 2n

We have two equations:

1) r - n = 10

2) r + 2n = 55

Solving these equations:

From r - n = 10:

⇒ r = n + 10

Substitute r in equation r + 2n = 55:

⇒ (n + 10) + 2n = 55

⇒ 3n + 10 = 55

⇒ 3n = 45

⇒ n = 15

The value of 'n' is 15.