CAT 2023 Slot 3 · Quant · Question 11

Work out the merchant's true cost and true revenue for each centimetre of cloth.

On buying, he pays for 100 cm but walks away with 105 cm.

So he pays ₹100 for 105 cm, making his cost \frac{100}{105} rupees per centimetre.

On selling, the list rate is ₹110 per metre, and a 5% discount brings the charge to 110\times 0.95=104.5 per billed metre.

But a billed metre is only 95 cm of actual cloth.

So he collects ₹104.5 for 95 cm, making his revenue \frac{104.5}{95}=1.1 rupees per centimetre.

The profit per centimetre is 1.1-\frac{100}{105}.

Now \frac{100}{105}=\frac{20}{21}\approx 0.95238, so the profit is about 0.14762 per centimetre.

As a percentage of cost, \frac{0.14762}{0.95238}=0.155.

That is a profit of 15.5% — the second option.

Shortcut. Both cheats and the discount are multiplicative, so chain them: \frac{110}{100}\times 0.95\times \frac{105}{95}=1.155. The profit factor is read off directly, giving 15.5% with no per-centimetre arithmetic.