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. 100
• B. 240
• C. 340
• D. None of Above

Answer 1

The Correct Option is C

Let initial stock of all the fruits is $S$ and we have $b$ and $a$ mangoes initially.
Stock of Mangoes $= 40\%$ of $S$ $= \frac {2S}{5}$
Total number of fruits sold = Mangoes Sold + Apples Sold + Bananas Sold
$= \frac {2S}{10} + 96 + \frac {4a}{10}= \frac S2$ (Given)

$⇒ \frac S5 +96+\frac {2a}{5}= \frac S2$

$⇒ S=\frac {4a+960}{3}$
$⇒ S=\frac {4a}{3}+320$
$a$ has to be multiple of $3$ for the above term to be an integer but $a$ has to be multiple of $5$ for $\frac {4a}{10}$ to be an integer.
⇒ Smallest value of $a$ satisfying both conditions is $15$.
$⇒ \frac {4a}{3}+320$

$⇒ \frac {4 \times 15}{3}+320$

$⇒ 20+320$
$⇒340$

So, the correct option is $(C): 340$