NinetynineCAT 2023 Slot 2 QA Q15 Percentages & Profit-Loss
Question 15 of the Quantitative Ability (QA) section, CAT 2023 Slot 2, with CAT's official answer and a worked solution.
Jayant bought a certain number of white shirts at the rate of Rs 1000 per piece and a certain number of blue shirts at the rate of Rs 1125 per piece. For each shirt, he then set a fixed market price which was 25% higher than the average cost of all the shirts. He sold all the shirts at a discount of 10% and made a total profit of Rs 51000. If he bought both colors of shirts, then the maximum possible total number of shirts that he could have bought is
TITA: type in the answer. There are no options and no negative marking.
Answer: 407 Percentages & Profit-Loss TITA
Solution
- Let total cost be \(C\) and the average cost \(\bar c\). Selling price per shirt \(= 0.9 \times 1.25\bar c = 1.125\bar c\), so the profit is \(0.125C\).
- \(0.125C = 51000 \Rightarrow C = 408000\), so \(1000w + 1125b = 408000\), i.e. \(8w + 9b = 3264\).
- To maximise \(w + b\), make the cheaper shirts (\(w\)) as many as possible, so take the smallest valid \(b \ge 1\).
- \(9b\) must be divisible by 8, so \(b\) is a multiple of 8. \(b = 8\) gives \(8w = 3192\), \(w = 399\). Total \(= 407\).