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.
- A1440
- B1176
- C1680
- D2520
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.
More Profit and Loss questions
- Q3Amal purchases some pens at ₹8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens…CAT 2021 Slot 1 · Quant · Profit and Loss
- Q18Raj invested ₹10000 in a fund. At the end of first year, he incurred a loss but his balance was more than ₹5000. This…CAT 2021 Slot 2 · Quant · Profit and Loss
- Q16A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the…CAT 2025 Slot 1 · Quant · Profit and Loss
- Q15An item with a cost price of ₹1650 is sold at a certain discount on a fixed marked price to earn a profit of 20% on…CAT 2025 Slot 2 · Quant · Profit and Loss
- Q5The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of…CAT 2025 Slot 3 · Quant · Profit and Loss
- Q21The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5…CAT 2024 Slot 1 · Quant · Profit and Loss
Take this paper as a timed test
Real exam timing, instant score, rank and topic-wise analysis.