The difference between the ages of two men is 10 years. 15 years ago, the…
2020
The difference between the ages of two men is 10 years. 15 years ago, the elder one was twice as old as the younger one. The present age of the elder man is
- A.
25 years
- B.
35 years
- C.
45 years
- D.
40 years
Attempted by 1 students.
Show answer & explanation
Correct answer: B
When a problem gives (1) the present difference between two people's ages and (2) a ratio between their ages at some point in the past, model it as a two-variable linear system: express one person's age in terms of the other using the given difference, then apply the ratio condition after shifting both ages back by the stated number of years. Solving that linear equation for the unknown gives both present ages.
Applying this to the given question:
Let the younger man's present age be Y. Since the age difference is 10 years, the elder man's present age is Y + 10.
Fifteen years ago, their ages were (Y + 10 − 15) = (Y − 5) for the elder and (Y − 15) for the younger.
The condition states the elder was twice as old as the younger at that time: (Y − 5) = 2(Y − 15).
Expand and solve: Y − 5 = 2Y − 30, so 2Y − Y = 30 − 5, giving Y = 25.
The elder man's present age is therefore Y + 10 = 25 + 10 = 35 years.
Check: with Y = 25, the elder is 35. Fifteen years ago they were 20 and 10 — and 20 is indeed twice 10, confirming both the age-difference and the timeline conditions are satisfied.