CAT 2022 Slot 1 · Quant · Question 9

CAT 2022 Slot 1 previous year question on Profit and Loss, with the answer and a step-by-step solution.

Profit and LossArithmeticMultiple choiceHard
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. A
    1440
  2. B
    1176
  3. C
    1680
  4. D
    2520
Pick an option, then check.
Answer & solution

Answer: Option C

The cost of 7 kg of cashews equals that of 30 kg of peanuts and of 9 kg of almonds, so set that common amount to a convenient figure.

Taking it as 630s for some scale s, the per-kg costs are \frac{630s}{7}=90s for cashews, \frac{630s}{30}=21s for peanuts and \frac{630s}{9}=70s for almonds.

Her total outlay is 4\times 90s+14\times 21s+6\times 70s.

That is 360s+294s+420s=1074s.

The total weight of the mixture is 4+14+6=24 kg.

If the whole 24 kg sold at the marked price M per kg, the profit would be ₹1752, so 24M-1074s=1752.

She actually sells 4 kg at M and the other 20 kg at 0.8M, so her revenue is 4M+20\times 0.8M=20M.

From the first relation, 24M=1752+1074s, so 20M=\frac{5}{6}\left( 1752+1074s \right).

Her actual profit is revenue minus cost: \frac{5}{6}\left( 1752+1074s \right)-1074s=1460+895s-1074s=1460-179s.

Setting this equal to ₹744 gives 179s=716, so s=4.

The almonds cost 6\times 70s=420\times 4=1680, that is ₹1680 — the third option.

Shortcut. Choosing the common cost as a multiple of \text{LCM}\left( 7,30,9 \right)=630 keeps every per-kg price a whole number, so no fractions appear until the final equation. Note also that selling 4 kg at full price and 20 kg at 20% off is the same revenue as selling 20 kg at full price.

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