CAT 2022 Slot 3 · Quant · Profit, Loss and Discount · medium

A trader buys two items for a total of ₹9,600. He sells the first at a profit of 20% and the second at a loss of 10%, and on the whole transaction…

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A trader buys two items for a total of ₹9,600. He sells the first at a profit of 20% and the second at a loss of 10%, and on the whole transaction makes neither profit nor loss. Find the cost price of the first item (in ₹).

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Answer: 3200

Let CP of first item = x, so CP of second = 9600 − x. Net profit = 0: 0.20x − 0.10(9600 − x) = 0 → 0.20x + 0.10x = 960 → 0.30x = 960 → x = 3200. Check: profit on item 1 = 0.20×3200 = 640; loss on item 2 = 0.10×6400 = 640 — these cancel, confirming no net profit or loss.

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