In a stock clearance sale, a shopkeeper gives 40% off on all his items. He incurs a loss of 25% by selling an item of marked price ₹2,000. Which one of the following is the cost price of this item?
- (a)₹1,800
- (b)₹1,200
- (c)₹1,600
- (d)₹1,400
Correct — C, ₹1,600. Work forward from the marked price. Forty per cent off ₹2,000 leaves a selling price of 0·6 × 2,000 = ₹1,200. That sale is said to involve a loss of 25 per cent, and a loss is always reckoned on the cost price, so the selling price is 75 per cent of cost: 1,200 = 0·75 × CP. Dividing, the cost price is 1,200 ÷ 0·75 = ₹1,600. Check it the other way — a quarter of 1,600 is 400, and 1,600 − 400 is 1,200, exactly the discounted price.
- (a)₹1,800 — Selling at 1,200 against a cost of 1,800 is a loss of 600, which is 33·3 per cent and not 25 per cent.
- (b)₹1,200 — This is the selling price itself. Cost and selling price coincide only when there is neither profit nor loss.
- (d)₹1,400 — Would make the loss 200 on 1,400, about 14·3 per cent. It is roughly what you get by taking 25 per cent off the wrong base, the selling price rather than the cost.
Three prices appear in these questions and each percentage attaches to a particular one. Discount is always a percentage of the marked price. Profit and loss are always percentages of the cost price. Selling price is what links them: marked price minus discount equals selling price, and cost price plus profit, or minus loss, equals the same selling price. Getting the base right is the whole discipline.
The useful shorthand is multipliers. A discount of d turns the marked price into (1 − d) times itself; a loss of l means the selling price is (1 − l) times the cost. Here the chain is 2,000 × 0·6 = 1,200 and 1,200 ÷ 0·75 = 1,600. Multiplying to go forwards and dividing to go backwards keeps the direction clear, which matters because reversing a percentage by subtracting it from the other side is the most frequent source of wrong answers in this topic.
- Discount is calculated on the marked price; profit and loss on the cost price.
- A 40 per cent discount on ₹2,000 gives a selling price of ₹1,200.
- A loss of 25 per cent means selling price = 0·75 × cost price.
- Cost price = 1,200 ÷ 0·75 = ₹1,600.
- Successive percentages multiply — they never add.
Taking the 25 per cent off the selling price instead of the cost gives ₹1,400, which is why that value is offered.
- Applying the loss percentage to the selling price rather than the cost price.
- Adding the discount and the loss percentages together.
- Treating the marked price as the cost price when no cost is stated.
A two-step percentage chain. Identify the base of each percentage before doing any arithmetic.
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 multiplier rule set as the whole question. Two ten-per-cent reductions leave 0·9 × 0·9 = 0·81 of the price, an effective discount of nineteen per cent rather than twenty — the same refusal of percentages to add that governs this item.
- practice — not a real PYQ
An article marked at ₹500 is sold at a discount of 20 per cent, giving the shopkeeper a profit of 25 per cent. Its cost price is
- (a)₹300
- (b)₹320
- (c)₹350
- (d)₹400
Answer(b) ₹320 — the selling price is 400, and 400 = 1·25 × cost.
- practice — not a real PYQ
Two successive discounts of 20 per cent and 10 per cent are equivalent to a single discount of
- (a)28 per cent
- (b)30 per cent
- (c)32 per cent
- (d)25 per cent
Answer(a) 28 per cent — 0·8 × 0·9 = 0·72, so 28 per cent comes off.