Darshan purchased 5 kg of apples out of which ${\frac{1}{4}}^{th}$ were found rotten. If the remaining apples were divided among 4 people, including Darshan, then what is the fraction of apples that Darshan got?

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Solution

Quantity of apples purchased = 5 kg
Quanity of apples found rotten = $\frac{5}{4}$ kg
$⟹$ Quanity of apples that weren't rotten = $(5 - \frac{5}{4})$ kg = $\frac{20 - 5}{4}$ kg = $\frac{15}{4}$ kg

Now, $\frac{15}{4}$ kg of apples are to be divided among 4 people.
$⟹$ Each person gets a share of $\frac{\frac{15}{4}}{4}$ kg of apples.
But, $\frac{\frac{15}{4}}{4} = \frac{15}{4} \times \frac{1}{4} = \frac{15}{16} .$
Thus, the fraction of apples that Darshan got is equal to $\frac{15}{16} .$

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