Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years…
2026
Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
- A.
16 years
- B.
18 years
- C.
20 years
- D.
Cannot be determined
Attempted by 7 students.
Show answer & explanation
Correct answer: A
Concept: In age-ratio problems, represent the ages of two people using a single common multiplier based on a known ratio at one time point (e.g. 6x and 5x for a 6 : 5 ratio). To find the ratio at another time point, add the elapsed years (future) or subtract them (past) from each person's age-in-terms-of-x, then set up and solve the resulting ratio equation.
Let the ages of Kunal and Sagar six years ago be 6x and 5x years respectively (using the given past ratio 6 : 5).
Present age of Kunal = 6x + 6 and present age of Sagar = 5x + 6 (adding back the 6 years).
Four years hence, Kunal's age = (6x + 6) + 4 = 6x + 10 and Sagar's age = (5x + 6) + 4 = 5x + 10.
Using the given future ratio: (6x + 10) / (5x + 10) = 11 / 10.
Cross-multiplying: 10(6x + 10) = 11(5x + 10) ⇒ 60x + 100 = 55x + 110 ⇒ 5x = 10 ⇒ x = 2.
Sagar's present age = 5x + 6 = 5(2) + 6 = 16 years.
Cross-check: Six years ago Kunal = 12, Sagar = 10, giving ratio 12 : 10 = 6 : 5 — matches. Four years hence Kunal = 22, Sagar = 20, giving ratio 22 : 20 = 11 : 10 — matches. Both conditions are satisfied, confirming Sagar's present age is 16 years.