CAT 2023 Slot 3 Solved Paper

Let us assume the initial stock of all the fruits is $\mathrm{S}$.
Let us take we have ' $\mathit{b}$ ' and 'a' mangoes initially.
Stock of Mangoes $=40\%$ of $\mathit{S}=2\mathit{S}∕5$
The total number of fruits sold are Mangoes Sold + Apples Sold + Bananas Sold
$=2\mathrm{S}/10+96+4\mathrm{a}/10=\mathrm{S}/2$ (Given)
$\Rightarrow \mathrm{S}/5+96+2\mathrm{a}/5=\mathrm{S}/2$
$\Rightarrow \mathrm{S}=\frac{\left(4\mathit{a}+960\right)}{3}$
$\Rightarrow \frac{4\mathit{a}}{3}+320$
'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 $4\mathit{a}/10$ to be an integer.
⇒ The smallest value of 'a' satisfying both conditions is 15 .
$\Rightarrow \frac{4\mathit{a}}{3}+320=\frac{4\left(15\right)}{3}+320=340$