Six years ago, the ratio of Kunal's age to Sagar's age was 6:5. Four years from now, it will be 11:10. What is Sagar's present age?

Problem restatementTwo time-shifted age ratios are given (6 years ago and 4 years hence). Write equations for present ages and solve.

Given data

• Present ages: Kunal = K, Sagar = S.
• (K − 6):(S − 6) = 6:5.
• (K + 4):(S + 4) = 11:10.

Concept/ApproachConvert each ratio to a linear equation and solve the simultaneous system.

Step-by-Step calculation5(K − 6) = 6(S − 6) ⇒ 5K − 30 = 6S − 36 ⇒ 5K = 6S − 6 …(1)10(K + 4) = 11(S + 4) ⇒ 10K + 40 = 11S + 44 ⇒ 10K = 11S + 4 …(2)From (1): K = (6S − 6)/5Plug in (2): 10×(6S − 6)/5 = 11S + 4 ⇒ 12S − 12 = 11S + 4 ⇒ S = 16

Verification/AlternativeThen K from (1): 5K = 6×16 − 6 = 90 ⇒ K = 18. Check: 6 years ago → (12:10) = 6:5; 4 years hence → (22:20) = 11:10. Works.

Common pitfallsDropping the time shifts (−6 and +4) when forming the equations.

Final Answer16 years