CAT 2020 Slot 2 QA Question & Solution
Question
Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10% profit. With no discounts, his percentage of profit would have been
Options
Solution
Let the cost price (CP) of each toy be $x$.
The total CP for 12 toys will be $12x$. Now, the shopkeeper made a 10% profit on CP, which means:
$$
12x(1.1) = 2112 \quad \text{or} \quad x = 160
$$
Hence, the CP of each toy is ₹160.
Let the selling price (SP) of each toy be $m$. Now, the shopkeeper sold 8 toys at a 20% discount, so the selling price for these 8 toys is:
$$
8m \times 0.8 = 6.4m
$$
He sold 4 toys at an additional 25% discount, so the selling price for these 4 toys is:
$$
4m \times 0.8 \times 0.75 = 2.4m
$$
Now, the total selling price is:
$$
6.4m + 2.4m = 8.8m = 2112 \quad \text{or} \quad m = 240
$$
Hence, the CP of each toy is ₹160, and the SP of each toy is ₹240. Thus, the profit percentage is:
$$
\frac{240 - 160}{160} \times 100 = 50%
$$
Hence, the profit percentage is 50%.