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CAT 2019 Slot 2 — QA Question 27

Profit & LossEasy

Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the remaining four at a loss of 25%. If he made a total profit of Rs. 2000, then his purchase price of a bicycle, in Rupees, was

Answer & solution

  • A

    2000

  • B

    6000

  • C

    8000

  • 4000

Solution

Easy

Six bicycles sell at +25%+25\% and four at −25%-25\%. Net profit per "matched" pair of a gain and a loss cancels; only the surplus profit-bicycles contribute. Set up one equation in the cost price.

1

Set up profit and loss. Let the cost price of one bicycle be xx. A 25%25\% profit gives +x4+\tfrac{x}{4} per cycle; a 25%25\% loss gives −x4-\tfrac{x}{4} per cycle.

Total profit=6⋅x4−4⋅x4(6 gains, 4 losses)⇒ 2000=6x−4x4=2x4=x2\begin{aligned} &\text{Total profit} = 6\cdot\frac{x}{4} - 4\cdot\frac{x}{4} \quad\text{(6 gains, 4 losses)}\\ &\Rightarrow\ 2000 = \frac{6x-4x}{4} = \frac{2x}{4} = \frac{x}{2} \end{aligned}
2

Solve for xx.

x2=2000⇒ x=4000\begin{aligned} &\frac{x}{2} = 2000\\ &\Rightarrow\ x = 4000 \end{aligned}
Purchase price=Rs. 4000\text{Purchase price}=\text{Rs. }4000
CAT 2019 Slot 2 QA Q27: Mukesh purchased 10 bicycles in 2017, all at the same price. He sold six of these at a profit of 25% and the r — Solution | TheCATExam