NinetynineCAT 2024 Slot 2 QA Q12 Percentages & Profit-Loss
Question 12 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, 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
- Let total \(= T\); mangoes \(= 0.4T\), apples \(= A\), bananas \(= 0.6T - A\).
- Sold: \(0.2T + 96 + 0.4A = 0.5T\), so \(A = 0.75T - 240\). Need \(A \ge 1 \Rightarrow T \ge 322\).
- Integer counts: half the mangoes \(0.2T\) must be an integer (\(T\) multiple of 5); \(A\) integer needs \(T\) multiple of 4; \(0.4A\) integer needs \(A\) multiple of 5. Together \(T\) is a multiple of 20.
- Smallest multiple of 20 that is at least 322 is 340: mangoes 136, apples 15, bananas 189 (at least 96, fine).
- Check: sold \(68 + 96 + 6 = 170 = \frac{340}{2}\). Answer 340.