CAT 2021 Slot 2 · Quant · Question 22

CAT 2021 Slot 2 previous year question on Averages, Mixture and Alligation, with the answer and a step-by-step solution.

Averages, Mixture and AlligationArithmeticMultiple choiceMedium

A person buys tea of three different qualities at ₹800, ₹500, and ₹300 per kg, respectively, and the amounts bought are in the proportion 2 : 3 : 5. She mixes all the tea and sells one-sixth of the mixture at ₹700 per kg. The price, in ₹ per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is

  1. A

    692

  2. B

    688

  3. C

    653

  4. D

    675

Pick an option, then check.
Answer & solution

Answer: Option B

Take a convenient batch of 10 kg, namely 2 kg, 3 kg and 5 kg.

Cost =2\times 800+3\times 500+5\times 300=1600+1500+1500=4600.

A 50\% overall profit means total revenue must be 1.5\times 4600=6900.

She sells \frac{10}{6}=\frac{5}{3} kg at 700 per kg, earning \frac{5}{3}\times 700=\frac{3500}{3}.

The rest must bring in 6900-\frac{3500}{3}=\frac{20700-3500}{3}=\frac{17200}{3}, spread over 10-\frac{5}{3}=\frac{25}{3} kg.

So the price is \frac{17200}{3}\div \frac{25}{3}=\frac{17200}{25}=688, that is ₹688 per kg.

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