CAT 2023 Slot 2 · Quant · Question 9

Track Minu's money through each step.

She buys at ₹1000 and sells to Kanu at a 20% profit, so that sale fetches 1000\times 1.2=1200.

Her gain on this first deal is 1200-1000=200, that is ₹200.

Kanu now sells back at a 20% loss on his own cost of ₹1200, so the price is 1200\times 0.8=960.

Minu therefore buys the sunglasses again for ₹960.

Let her final selling price to Tanu be P.

Her total profit across everything is 200+\left( P-960 \right), and this equals ₹500.

So P-960=300, giving P=1260.

The profit on the last transaction alone is \frac{1260-960}{960}=\frac{300}{960}.

That is 0.3125, which is 31.25% — the second option.

Shortcut. The first deal is already worth ₹200, so the last one must supply the remaining ₹300. Against a cost of ₹960, that is \frac{300}{960}=\frac{5}{16}, and \frac{5}{16} is 31.25% — a fraction worth recognising on sight.