The single discount equivalent to the discount series of 15%, 20% and 5% is:

Correct — A. Successive discounts multiply the fraction that survives; they do not add.

After 15%, the price left is 0.85 of the list.
After a further 20%: 0.85 × 0.80 = 0.68.
After a further 5%: 0.68 × 0.95 = 0.646.

The customer pays 64.6% of the list price, so the single equivalent discount is 1 − 0.646 = 0.354 = 35.4% → option (a).

Why the others are wrong

• (b)
  20% — 20% is one of the three discounts copied out, not their combined effect. A single 20% leaves 0.80 of the list price, where the chain leaves 0.646.
• (c)
  32% — 32% is the equivalent of the first two discounts only: 0.85 × 0.80 = 0.68, a 32% cut. The 5% step has been dropped.
• (d)
  32.5% — 32.5% would mean the customer pays 67.5% of the list price. The three surviving fractions multiply to 0.646, that is 64.6%, not 0.675.

For a discount series, work with what remains rather than with what is taken off.

A discount of d% leaves a factor of (1 − d⁄100), and successive discounts multiply those factors in any order: 0.85 × 0.80 × 0.95 = 0.646.

The single equivalent discount is 1 minus that product. It is always smaller than the sum of the discounts — 40% here — because each later cut is charged on an already reduced price.

Key facts

• A d% discount leaves a factor of (1 − d⁄100), and successive discounts multiply these factors.
• 0.85 × 0.80 × 0.95 = 0.646, so 15%, 20% and 5% together equal a single discount of 35.4%.
• Two discounts of a% and b% combine to a + b − ab⁄100.
• The equivalent single discount is always less than the arithmetic sum of the discounts.

Common traps

• Adding 15 + 20 + 5 to get 40%.
• Stopping after two discounts at 32%.
• Charging the 5% on the list price rather than on the already discounted price.

No directly related past PYQ was found.