A shopkeeper gives two consecutive discounts of 10% and 5% respectively on his items. He then adds 20% GST on his items. If an item has marked price ₹2,000, how much more or less of the actual price of the item a customer has to pay?
- (a)2.6% less
- (b)2.6% more
- (c)Same price
- (d)5.2% more
Correct — B, 2.6% more. Work in multipliers and the item takes one line. A 10 per cent discount multiplies by 0.90, a further 5 per cent discount multiplies by 0.95, and 20 per cent GST on the discounted figure multiplies by 1.20. Together 0.90 × 0.95 × 1.20 = 1.026, so a marked price of ₹2,000 becomes ₹2,052. Step by step it is the same: 2,000 less 10 per cent is 1,800; 1,800 less 5 per cent is 1,710; 1,710 plus 20 per cent is 2,052. The customer pays ₹52 more than the marked price, and 52 out of 2,000 is 2.6 per cent.
- (a)2.6% less — The right magnitude with the comparison reversed. The final multiplier is 1.026, which is greater than one; a candidate who computes 2,052 and then subtracts in the wrong order gets the sign wrong.
- (c)Same price — This assumes the two discounts cancel the tax. They do not — successive cuts of 10 and 5 per cent take 14.5 per cent off, and adding 20 per cent back to the smaller base still lands above the marked price.
- (d)5.2% more — That would need the customer to pay ₹2,104, and no route through these figures produces it. The number is the correct excess doubled — a trap for anyone who has found 2.6 and is no longer checking against which price it is measured.
Successive percentage changes multiply; they do not add. A discount of x per cent is a multiplier of (1 − x/100), a tax of y per cent is a multiplier of (1 + y/100), and the order in which they are applied does not matter because multiplication commutes. The single equivalent change is the product of the multipliers minus one.
Two traps are built in. The first is adding 10 and 5 to get a 15 per cent discount, which overstates the reduction: the true combined discount is 10 + 5 − (10 × 5)/100 = 14.5 per cent. The second is the base for the final comparison. The GST is charged on the discounted price, but the question asks how the customer's payment compares with the marked price of ₹2,000, so the answer must be measured against 2,000 and not against 1,710.
- Successive discounts of a and b per cent give a single equivalent discount of a + b − ab/100.
- Ten and five per cent combine to 14.5 per cent, not 15.
- The full chain here is 0.90 × 0.95 × 1.20 = 1.026.
- Marked price ₹2,000 becomes ₹1,800, then ₹1,710, then ₹2,052.
- The excess of ₹52 measured on ₹2,000 is 2.6 per cent.
One product does the same work: 0.90 × 0.95 × 1.20 = 1.026.
- Adding 10 and 5 into a single 15 per cent discount.
- Measuring the final excess against the discounted price of ₹1,710 rather than the marked price.
A multiplier chain dressed as a shopping problem; the only real decision is which price the comparison is against.
A person buys an item from a shop for which the shopkeeper offers a discount of 10% on the marked price. The person pays using an e-wallet which gives 10% cash back. Which one of the following is the value of effective discount?
- (a) 20%
- (b) 18%
- (c) 19%
- (d) 21%
Answer(c) 19%
The same multiplier rule with the tax removed. Two cuts of 10 per cent give 0.90 × 0.90 = 0.81, an effective discount of 19 rather than 20 — the identical reason two discounts here come to 14.5 and not 15.
- practice — not a real PYQ
Two successive discounts of 20% and 10% are equivalent to a single discount of
- (a)30%
- (b)28%
- (c)26%
- (d)25%
Answer(b) 28% — 0.80 × 0.90 = 0.72, so 28 per cent comes off, not 30.
- practice — not a real PYQ
A price is raised by 25% and then reduced by 20%. The net change is
- (a)5% increase
- (b)5% decrease
- (c)No change
- (d)1% increase
Answer(c) No change — 1.25 × 0.80 = 1.00, so the price returns to where it started.