If the successive discount by 10%,15%, then the single equivalent rate of discount is:

Correct — C. Take the marked price as ₹100 and apply the two cuts in order.

10% off ₹100: 100 − 10 = ₹90
15% off ₹90: 90 − 13.50 = ₹76.50
Removed in all: 100 − 76.50 = ₹23.50 from ₹100, which is 23.5% → option (c)

Formula route: a + b − ab⁄100 = 10 + 15 − (10 × 15)⁄100 = 25 − 1.5 = 23.5%.

Why the others are wrong

• (a)
  24.2% — 24.2% is unreachable from these rates. The equivalent must sit exactly ab⁄100 = 1.5 points below the plain sum of 25%, and 25 − 1.5 is 23.5.
• (b)
  43.4% — 43.4% is above the plain sum 10 + 15 = 25%. Successive discounts always remove less than the sum, so anything over 25% is out on sight.
• (d)
  32.3% — 32.3% also breaks the 25% ceiling set by 10 + 15. The equivalent rate is the sum minus ab⁄100, so it lands just under 25 and can never approach a third off.

The second discount is charged on the already reduced price, not on the marked price. That single fact is the whole topic.

Because 15% of ₹90 is less than 15% of ₹100, the pair removes less than 10 + 15 = 25%. The shortfall is the overlap — 15% of the 10% already taken off — which is ab⁄100 = 1.5 points.

That gives the standard form: a single equivalent discount of a + b − ab⁄100 per cent. It is symmetric, so 15% then 10% removes the same 23.5%.

Key facts

• Successive discounts of a% and b% equal a single discount of (a + b − ab⁄100)%.
• For 10% and 15% this is 25 − 1.5 = 23.5%.
• The equivalent single discount is always smaller than a + b, because the second cut falls on a reduced price.
• Order does not matter: ₹100 → ₹85 → ₹76.50 gives the same ₹76.50.

Common traps

• Adding the rates to 25% and picking the nearest option
• Taking the second discount on the marked price instead of the reduced one
• Using a + b + ab⁄100, which is the successive-increase formula

No directly related past PYQ was found.