CAT 2021 Quant was dominated by Arithmetic followed by Algebra. In Arithmetic, the questions were dominated by topics like **Speed-time-distance**, **Mixture and Alligations**. This year, there was a surprise. The questions from **Geometry** were relatively on the lower side as compared to the previous years. There were 8 TITA Qs this year. Overall this section was at a medium level of difficulty.

Question 22 : 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 INR per kg, at which she should sell the remaining tea, to make an overall profit of 50%, is

- 692
- 688
- 653
- 675

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Tea of three different qualities costing ₹ 800, ₹ 500, and ₹ 300 per kg, respectively, is bought in amounts which are in the proportion 2 : 3 : 5.

Let us assume that the amounts in which the Tea is bought is 6 : 9 : 15

(This is because 2 + 3 + 5 = 10, which is not a multiple of 6, further reading into the question, we find that we need to deal with one-sixth of the quantity, so having the total quantity as a multiple of 6 is beneficial to us.)

So, Total Cost Price = ₹ 800 * 6 + ₹ 500 * 9 + ₹ 300 * 15 = ₹ 13,800

Profit % = 50%

Profit = 50% of Cost Price = 50% of ₹ 13,800 = ₹ 6,900

Therefore, Selling Price = Cost Price + Profit = ₹ 13,800 + ₹ 6,900 = ₹ 20,700

Since one-sixth that \\frac{1}{6})(6 + 9 + 15) = \\frac{1}{6})(30) = 5kgs is sold at ₹ 700 per kg.

The Selling Price of these 5kgs is 5 * 700 = ₹ 3,500

The remaining ₹ 20,700 - ₹ 3,500 = ₹ 17,200 must be generated from selling the remaining 30 - 5 = 25 kgs.

So, the selling price of the remaining tea per kg must be \\frac{17,200}{25}) = 172 * 4 = ₹ 688 per kg

Choice B is the correct answer.

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