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 \((C): 340\)