A shopkeeper sold a product at 30% loss. Had his selling price been ₹150 more, he would have made a profit of 10%. What was the cost price?

Correct — A, ₹375. Let the cost price be C. Selling at a 30 per cent loss means the actual selling price was 0.70C. Selling for ₹150 more would have produced a 10 per cent profit, that is 1.10C. So 0.70C + 150 = 1.10C, which gives 150 = 0.40C and C = ₹375. The check runs in one line: 70 per cent of 375 is ₹262.50, adding ₹150 gives ₹412.50, and ₹412.50 is exactly 110 per cent of ₹375.

• (b)₹400 — At a cost of ₹400 the two selling prices would be ₹280 and ₹440, a gap of ₹160 rather than ₹150.
• (c)₹425 — The gap between a 30 per cent loss and a 10 per cent profit on ₹425 is 40 per cent of 425, which is ₹170.
• (d)₹450 — ₹450 comes from treating ₹150 as one-third of the cost price. The gap of 40 percentage points on ₹450 is ₹180.

Profit and loss percentages are always taken on the cost price unless a question says otherwise. A 30 per cent loss puts the selling price at 70 per cent of cost, a 10 per cent profit puts it at 110 per cent, and the difference between the two scenarios is 40 per cent of the cost. Whenever a question supplies the rupee value of a change in selling price, that value can be equated to the percentage-point gap.

The one-line form is worth drilling: change in selling price ÷ change in percentage = cost price ÷ 100. Here ₹150 ÷ 40 per cent gives ₹375 straight away. The commonest error is to take the percentages on the selling price instead of the cost, which produces the wrong base and one of the larger options. Note that the second selling price never happened — the stem describes it as what would have followed, which is the language of a comparison rather than a second sale.

• Selling price at a loss of L per cent is (100 − L)/100 of the cost price.
• Selling price at a profit of P per cent is (100 + P)/100 of the cost price.
• A move from a 30 per cent loss to a 10 per cent profit is a swing of 40 per cent of the cost price.
• Cost price = (change in selling price × 100) ÷ (change in percentage), here 150 × 100 ÷ 40 = 375.
• Profit and loss percentages are reckoned on cost price by default, not on selling price.

• Taking the percentages on the selling price rather than the cost price.
• Adding 30 and 10 to get 40 per cent of the selling price instead of the cost price.
• Assuming both sales actually took place and averaging the two prices.

A standard profit-and-loss item where a rupee difference is matched against a percentage-point difference, solvable in one step once both prices are written on the same base.

• practice — not a real PYQ

  An article sold at a 20 per cent loss would have fetched a 5 per cent profit for ₹100 more. What is its cost price?

  • (a)₹300
  • (b)₹400
  • (c)₹450
  • (d)₹500

  Answer(b) ₹400 — the swing from 80 per cent to 105 per cent of cost is 25 per cent, so 0.25C = 100 and C = ₹400.

• practice — not a real PYQ

  A shopkeeper sells an item for ₹1,320 at a 10 per cent profit. What was the cost price?

  • (a)₹1,150
  • (b)₹1,200
  • (c)₹1,250
  • (d)₹1,300

  Answer(b) ₹1,200 — cost price = 1320 ÷ 1.10 = ₹1,200, and 10 per cent of 1,200 is the ₹120 of profit.