Twice the age of X is thrice the age of Y. 8 years back, the difference…
2025
Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 18 years. What is the present age of X?
- A.
24
- B.
54
- C.
56
- D.
91
Attempted by 8 students.
Show answer & explanation
Correct answer: B
Concept: The difference between two people's ages stays constant at every point in time — in the past, present, or future. When ages are given as a ratio (X : Y = a : b), the present ages can be written as X = aR and Y = bR for a common multiplier R; R is found by matching the ratio's difference, (a − b)R, to any known actual age difference, since that difference never changes with time.
Application:
Twice the age of X equals thrice the age of Y, so 2X = 3Y, which gives X : Y = 3 : 2.
Let the present ages be X = 3R and Y = 2R, for some positive number R.
Since the age difference is constant over time, the difference 8 years ago equals the present difference: 3R − 2R = 18, so R = 18.
Present age of X = 3R = 3 × 18 = 54 years.
Cross-check:
Y = 2R = 36. Eight years back, X was 46 and Y was 28 — the difference is 46 − 28 = 18, matching the given data. Also, 2 × 54 = 108 = 3 × 36, confirming the original ratio condition.