CAT 2022 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 9 : Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is

- 1440
- 1176
- 1680
- 2520

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Ankita had 4 kg cashews, 14 kg peanuts and 6 kg almonds.

In all, she had 24 kgs of nuts to sell. Let us assume the average buying price of these nuts is x rupees per kg.

*Average buying price means, Whatever the per kg cost of cashews, peanuts and almonds is, when you mix 4 kg cashews, 14 kg peanuts and 6 kg almonds and get 24 kgs of nuts, let's assume each kg of nuts cost x rupees per kg.*

Ankita planned to make a total profit of ₹1752 by selling these 24 kgs of nuts. That means, she planned on making a profit of \( \frac { 1752 } { 24 } \) = ₹73 on these 24 kgs of nuts. So the marked price of these 24 kgs of nuts is ₹‘x + 73’ per kg.

She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744.

This means,

4(x + 73) + 0.8 * 20(x + 73) = 24 x + 744

716 = 4x

x = 179

That means the buying price of 24 kgs of these nuts is 24x = 24(179) = ₹4296

In other words, the buying price of 4 kg cashews, 14 kg peanuts and 6 kg almonds is ₹4296.

We are told that “**the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds**.”

7C = 30 P = 9 A

Where C, P and A are the per kg buying costs of Cashews, Peanuts and Almonds respectively.

Let 7C = 30 P = 9 A = 630k

C = 90k

P = 21k

A = 70k

We know that, the buying price of 4 kg cashews, 14 kg peanuts and 6 kg almonds is ₹4296.

4 C + 14 P + 6 A = 4296

4 (90k) + 14 (21k) + 6 (70k) = 4296

360k + 294k + 420k = 1074k = 4296

k = 4

A = 70k = 280

The buying price of Cashews is ₹280 per kg.

The total money spent on Cashews is 6C = ₹1680

Choice C is the correct answer.

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