NinetynineCAT 2023 Slot 3 QA Q14 Percentages & Profit-Loss
Question 14 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.
A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes make up 40% of his stock. That day, he sells half of the mangoes, 96 bananas and 40% of the apples. At the end of the day, he ends up selling 50% of the fruits. The smallest possible total number of fruits in the stock at the beginning of the day is
TITA: type in the answer. There are no options and no negative marking.
Answer: 340 Percentages & Profit-Loss TITA
Solution
- Total T: mangoes \(0.4T\), bananas B, apples A with \(A+B=0.6T\).
- Sold: \(0.2T + 96 + 0.4A = 0.5T \Rightarrow A = 0.75T-240\), so \(B = 240-0.15T\).
- Integrality: half the mangoes (\(0.2T\)) needs \(5\mid T\); \(0.75T\) needs \(4\mid T\); so \(T\) is a multiple of 20. Also \(A\ge1 \Rightarrow T>320\).
- T = 340: mangoes 136, apples 15 (sell 6), bananas 189 (sell 96). Sold \(68+96+6=170 = 50\%\). Answer 340.