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CAT 2017 Slot 2 — QA Question 9

Profit & LossEasy

Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?

Answer & solution

Correct answer: 50

  • 50

  • B

    30

  • C

    25

  • D

    45

Solution

Easy

Equal counts of two candy types means xx dozen of each. Write total cost and total revenue per the per-dozen prices, set profit =150=150, and solve for the combined quantity.

1

Set up cost and revenue. Buy xx dozen at Rs 1515 and xx dozen at Rs 1212; sell all 2x2x dozen at Rs 16.5016.50.

CP=15x+12x=27xSP=16.5×2x=33x\begin{aligned} &\text{CP}=15x+12x=27x\\ &\text{SP}=16.5\times 2x=33x \end{aligned}
2

Apply the profit. Profit == SP −- CP =150=150.

33x−27x=150⇒ 6x=150 ⇒ x=25\begin{aligned} &33x-27x=150\\ &\Rightarrow\ 6x=150\ \Rightarrow\ x=25 \end{aligned}
3

Total dozens. He bought 2x2x dozen altogether.

2×25=50\begin{aligned} &2\times 25=50 \end{aligned}
Total=50 dozen\text{Total}=50\ \text{dozen}

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CAT 2017 Slot 2 QA Q9: Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sell — Solution | TheCATExam