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
Question:
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
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
Options
Answer: 340
Explanation:
Mangoes sold = 0.2x, apples sold = 0.4a, bananas = 96 → total sold = 0.5x 0.2x + 0.4a + 96 = 0.5x → 0.3x − 0.4a = 96 → 3x − 4a = 960 x must be divisible by 5, a multiple of 5 → try smallest a=15: x = (960 + 4×15)/3 = 1020/3 = 340
Explanation:
Mangoes sold = 0.2x, apples sold = 0.4a, bananas = 96 → total sold = 0.5x 0.2x + 0.4a + 96 = 0.5x → 0.3x − 0.4a = 96 → 3x − 4a = 960 x must be divisible by 5, a multiple of 5 → try smallest a=15: x = (960 + 4×15)/3 = 1020/3 = 340
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