CAT 2020 Quant Question [Slot 2] with Solution 13

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

  1. 60
  2. 55
  3. 50
  4. 54
Option: 3
Solution:

Let the cost price and marked price of each toy be c and m respectively.

Overall selling price \( = 8(0.8m) + 4\left( {\frac{3}{4} \times 0.8m} \right)\) i.e 8.8m.

Given, \(110\% \) of \(12c = 8.8m\)

\( \Rightarrow c = \frac{{2m}}{3}\)

\(\therefore \) Overall \(CP = 12 \times \frac{{2m}}{3}\) i.e 8m

Required profit percentage \( = \frac{{12m - 8m}}{{8m}} \times 100 = 50\% \)

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