CAT 2022 Question Paper | Quant Slot 1

CAT Previous Year Paper | CAT Quant Questions | Question 9

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

1. 1440
2. 1176
3. 1680
4. 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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