Ram’s income is 2.5% more than Shyam’s income. By what percentage is Shyam’s income less than Ram’s income?

Correct — D. Set Shyam's income at 100.

Ram = 100 + 2.5% of 100 = 102.5
Gap = 102.5 − 100 = 2.5
Shyam is short by 2.5 measured against Ram's 102.5, not against his own 100.
2.5 ⁄ 102.5 × 100 = 250 ⁄ 102.5 = 2.439%

SSC prints that value as 2.43% — option (d). Every other choice is a full percentage point away.

Why the others are wrong

• (a)
  4.43% — 4.43% — reverse it and check: if Shyam were 4.43% below Ram, Ram would stand 4.43 ⁄ 95.57 × 100 = 4.64% above Shyam, not the 2.5% the question states.
• (b)
  1.43% — 1.43% — reversing gives 1.43 ⁄ 98.57 × 100 = 1.45% above Shyam, barely half of the 2.5% you were given to start from.
• (c)
  3.43% — 3.43% — reversing gives 3.55%. The reverse of a rise is always a shade smaller than the rise, so any figure above 2.5% is wrong before you compute it.

Percentage comparisons are directional. "Ram is 2.5% more than Shyam" measures the gap against Shyam's income; "Shyam is less than Ram" measures the same gap against Ram's.

Ram is the larger number, so the same absolute gap of 2.5 is a smaller fraction of it. The reverse figure is therefore always a little under 2.5%, never equal to it.

The standard form: if A is x% more than B, then B is 100x ⁄ (100 + x) % less than A. With x = 2.5 that is 250 ⁄ 102.5 = 2.439…%.

Key facts

• If A is x% more than B, then B is 100x ⁄ (100 + x) % less than A.
• A 2.5% rise reverses to a 2.439…% fall, because the base grows from 100 to 102.5.
• The reverse of a percentage increase is always smaller than the increase itself.

Common traps

• Answering 2.5% by dividing the gap by Shyam's income instead of Ram's.
• Computing 2.44% correctly and then rejecting every option because none of them says 2.44%.

No directly related past PYQ was found.