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
Correct Answer: 340
Let us assume the initial stock of all the fruits is S.
Let us take we have 'b' and 'a' mangoes initially.
Stock of Mangoes = 40% of S = 2S/5
The total number of fruits sold are Mangoes Sold + Apples Sold + Bananas Sold
= 2S/10 + 96 + 4a/10 = S/2 (Given)
=> S/5 + 96 + 2a/5 = S/2
=> S = $$\dfrac{\left(4a+960\right)}{3}$$
=> $$\dfrac{4a}{3}+320$$
'a' has to be a multiple of 3 for the above term to be an integer.
But 'a' has to be a multiple of 5 for 4a/10 to be an integer.
=> The smallest value of 'a' satisfying both conditions is 15.
=> $$\dfrac{4a}{3}+320=\dfrac{4\left(15\right)}{3}+320$$ = 340
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