Ghanshyam is thrice as old as Akash. 10 years ago, Ghanshyam was four times as old as Akash. What is the difference between their current ages (in years)?

Correct — B. Let Akash be A years old now, so Ghanshyam is 3A.

Ten years ago: Ghanshyam = 3A − 10, Akash = A − 10
The condition is 3A − 10 = 4(A − 10)
3A − 10 = 4A − 40
40 − 10 = 4A − 3A, so A = 30

Akash is 30, Ghanshyam is 3 × 30 = 90.
Difference = 90 − 30 = 60 → option (b).

Why the others are wrong

• (a)
  65 — 65 is odd, and the difference is 2A (3A − A), which is even for any whole-number age. Reaching 65 would need Akash to be 32.5.
• (c)
  50 — 50 needs A = 25 and Ghanshyam 75. Ten years ago that is 65 and 15, and 65 is not four times 15 — it is 4.33 times.
• (d)
  55 — 55 is odd for the same reason 65 fails: the gap is twice Akash's age, so it can never come out odd.

Two statements, one unknown. "Thrice as old" fixes the ratio now, "four times as old" fixes a different ratio at a different moment, and one variable is enough to carry both.

Set the younger age as A, write everyone else in terms of A, then subtract the same 10 years from both people. That subtraction is the step candidates skip.

A free check at the end: the difference 3A − A = 2A is twice the younger age, so it has to be even.

Key facts

• Ages move together: subtract the same number of years from every person named in the problem.
• A ratio now plus a different ratio at another time gives one equation in one unknown.
• The difference between two people's ages never changes, even though their ratio does.

Common traps

• Subtracting 10 from Ghanshyam only and leaving Akash untouched
• Answering 90 or 30 when the question asked for the difference
• Applying "four times as old" to the present instead of ten years ago

No directly related past PYQ was found.