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CAT 2019 Slot 2 — QA Question 33

Profit & LossEasy

A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a loss of 20%, respectively. Amal sells his table to Bimal at a profit of 30%, while Asim sells his table to Barun at a loss of 30%. If the amounts paid by Bimal and Barun are x and y, respectively, then (x - y) / p equals

Answer & solution

Correct answer: 1

  • 1

  • B

    1.2

  • C

    0.7

  • D

    0.5

Solution

Easy

Chain the multipliers. Amal's branch is +20%+20\% then +30%+30\%; Asim's branch is −20%-20\% then −30%-30\%. Express xx and yy as multiples of pp and subtract.

1

Bimal's price xx. Shopkeeper →\to Amal at +20%+20\%, then Amal →\to Bimal at +30%+30\%.

x=p×1.2×1.3=1.56 p\begin{aligned} &x = p\times 1.2\times 1.3 = 1.56\,p \end{aligned}
2

Barun's price yy. Shopkeeper →\to Asim at −20%-20\%, then Asim →\to Barun at −30%-30\%.

y=p×0.8×0.7=0.56 p\begin{aligned} &y = p\times 0.8\times 0.7 = 0.56\,p \end{aligned}
3

Compute the ratio.

x−yp=1.56 p−0.56 pp=1.00 pp=1\begin{aligned} &\frac{x-y}{p} = \frac{1.56\,p - 0.56\,p}{p} = \frac{1.00\,p}{p} = 1 \end{aligned}
x−yp=1\frac{x-y}{p} = 1

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CAT 2019 Slot 2 QA Q33: A shopkeeper sells two tables, each procured at cost price p, to Amal and Asim at a profit of 20% and at a los — Solution | TheCATExam