Chocolate Box Pricing and Weight Comparison

CAT 2021 Slot 2 · QA · Medium · Percentages

Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to

  1. A.

    127

  2. B.

    135

  3. C.

    124

  4. D.

    144

Answer

A

Explanation

Let the price of the small box be PSP_S and its weight be WSW_S. Then the price of the large box is PL=2PSP_L = 2 P_S. Let its weight be WLW_L.

Selling price per gram in small box =PSWS= \frac{P_S}{W_S}. Selling price per gram in large box =PLWL=2PSWL= \frac{P_L}{W_L} = \frac{2 P_S}{W_L}.

Given that 2PSWL=0.88×PSWS\frac{2 P_S}{W_L} = 0.88 \times \frac{P_S}{W_S}: 2WL=0.88WS    WLWS=20.88=20088=25112.2727\frac{2}{W_L} = \frac{0.88}{W_S} \implies \frac{W_L}{W_S} = \frac{2}{0.88} = \frac{200}{88} = \frac{25}{11} \approx 2.2727

The percentage by which WLW_L exceeds WSW_S is: (WLWSWS)×100%=(2.27271)×100%=127.27%\left(\frac{W_L - W_S}{W_S}\right) \times 100\% = (2.2727 - 1) \times 100\% = 127.27\% Nearest integer is 127127.

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