The difference between a discount of 25% and two successive discounts of 15% and 20% on a certain bill was ₹28. Find the amount of the bill.

Correct — B. Work with what is paid, not with what is deducted, and the two schemes line up on the same base.

A single 25% discount leaves 0.75 of the bill.
Successive 15% then 20% leaves 0.85 × 0.80 = 0.68 of the bill.

So the two schemes differ by 0.75 − 0.68 = 0.07 of the bill, and the question says that gap is ₹28.

0.07 × Bill = 28
Bill = 28 ⁄ 0.07 = ₹400 → option (b).

Why the others are wrong

• (a)
  ₹500 — ₹500 makes the 7% gap worth ₹35, not ₹28. Working backwards, ₹28 out of ₹500 is 5.6%, and no pairing of these discounts produces 5.6%.
• (c)
  ₹450 — ₹450 makes the 7% gap ₹31.50. The gap is a fixed 7% of the bill, so exactly one bill makes it ₹28, and 28 ⁄ 0.07 gives ₹400.
• (d)
  ₹550 — ₹550 makes the 7% gap ₹38.50, well past ₹28. It is the largest option and the furthest from the requirement.

Successive discounts multiply, they do not add. Two discounts of a% and b% leave (1 − a⁄100)(1 − b⁄100) of the marked price, so 15% then 20% leaves 0.85 × 0.80 = 0.68 and is equivalent to a single discount of 32%.

Once both schemes are written as a fraction of the same bill, their difference is a fixed percentage of that bill. Turning the rupee difference into a percentage difference and dividing is the whole method.

The order of the two discounts does not matter, since multiplication commutes.

Key facts

• Two successive discounts of a% and b% are equivalent to a single discount of a + b − ab⁄100 per cent.
• For 15% and 20% that single equivalent is 32%, so the customer pays 0.68 of the bill.
• The gap between a 25% discount and a 32% discount is 7% of the bill, and 7% of ₹400 is ₹28.

Common traps

• Adding 15 and 20 to 35%, which gives a 10% gap and a bill of ₹280.
• Applying the 7% to the discount amount instead of to the bill.
• Assuming the larger discount comes first changes the result, when order is irrelevant.

No directly related past PYQ was found.