Toy Discount and Profit

CAT 2020 Slot 2 · QA · Easy · Arithmetic

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Anil buys 12 toys and labels each with the same selling price. He sells 8 toys initially at 20%20\% discount on the labeled price. Then he sells the remaining 4 toys at an additional 25%25\% discount on the discounted price. Thus, he gets a total of Rs 2112, and makes a 10%10\% profit. With no discounts, his percentage of profit would have been

  1. A.

    60

  2. B.

    50

  3. C.

    55

  4. D.

    54

Answer

B

Explanation

Let LL be the labeled price of one toy. 8 toys are sold at 20%20\% discount   ⟹  0.8L\implies 0.8 L per toy. 4 toys are sold at an additional 25%25\% discount   ⟹  0.8L×0.75=0.6L\implies 0.8 L \times 0.75 = 0.6 L per toy. Total revenue = 8(0.8L)+4(0.6L)=6.4L+2.4L=8.8L=21128(0.8L) + 4(0.6L) = 6.4L + 2.4L = 8.8L = 2112. L=21128.8=240L = \frac{2112}{8.8} = 240 Total Cost Price (CP) for 12 toys: Revenue=1.10×CP  ⟹  2112=1.10×CP  ⟹  CP=1920\text{Revenue} = 1.10 \times \text{CP} \implies 2112 = 1.10 \times \text{CP} \implies \text{CP} = 1920 Cost price per toy = 192012=160\frac{1920}{12} = 160. With no discount, selling price per toy = L=240L = 240. Profit percentage = 240−160160×100%=80160×100%=50%\frac{240 - 160}{160} \times 100\% = \frac{80}{160} \times 100\% = 50\%.

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