The current average age of Sohan, Mohan, and Rohan is 30 years. 10 years from now, the ratio of the ages of Sohan and Mohan will be 17:16 respectively, and 6 years ago, the ratio of their ages was 11:10 respectively. What is the present age of Rohan?

Let present ages be:

Sohan = S, Mohan = M, Rohan = R

Average age = 30

S + M + R = 3 × 30 = 90 ...(1)

After 10 years, ratio S : M = 17 : 16

(S + 10) / (M + 10) = 17 / 16

⇒ 16(S + 10) = 17(M + 10)

⇒ 16S − 17M = 10 ...(2)

Six years ago, ratio S : M = 11 : 10

(S − 6) / (M − 6) = 11 / 10

⇒ 10(S − 6) = 11(M − 6)

⇒ 10S − 11M = −6 ...(3)

Solve (2) and (3):

From (2): 16S − 17M = 10

From (3): 10S − 11M = −6

Multiply (2) by 5: 80S − 85M = 50

Multiply (3) by 8: 80S − 88M = −48

Subtract: (80S − 85M) − (80S − 88M)

⇒ 3M = 98 ⇒ M = 98/3

Put M in (3):

10S − 11 × (98/3) = −6

10S = 1060/3 ⇒ S = 106/3

Now use (1):

S + M + R = 90

(106/3) + (98/3) + R = 90

204/3 + R = 90

68 + R = 90 ⇒ R = 22

Answer: Rohan’s present age = 22 years.