A farmer bought $100$ hens for $₹ 4000$ , sells $20$ of them at a gain of $5 %$ . At what gain $%$ must he sell so as to gain $20 %$ on the whole?

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Solution

From question,
Price of $100$ hen $= ₹ 4000$
Price of $1$ hen $= \frac{4000}{100} = ₹ 40$
He sells $20$ hens at a gain of $5 %$
So, selling price of those $20$ hens $= 20 \times [\frac{100 + P r o f i t %}{100} \times C . P]$
$= 20 \times [\frac{100 + 5}{100} \times 40]$
$= 20 \times [\frac{105}{100} \times 40]$
$= 20 \times [\frac{105}{5} \times 2]$
$= 20 \times [21 \times 2]$
$= 20 \times 42$
$= ₹ 840$
On the whole he wants $20 %$ profit which means the profit he wants $= \frac{20}{100} \times 4000$
$= 20 \times 40$
$= ₹ 800$
Price of $80$ hens $= 80 \times 40 = ₹ 3200$
From $₹ 800$ he already got Profit Of $₹ 40$ Which Means he has to get More $₹ 760$
Gain Percentage $(%) = \frac{P r o f i t}{C . P} \times 100$
$= \frac{760}{3200} \times 100$
$= \frac{19}{8}$
$= 23.75 %$
Hence, the required gain percentage $= 23.75 %$

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A farmer bought 100 hens for ₹4000, sells 20 of them at a gain of 5%. At what gain % must he sell so as to gain 20% on the whole?

A farmer bought $100$ hens for $₹ 4000$ , sells $20$ of them at a gain of $5 %$ . At what gain $%$ must he sell so as to gain $20 %$ on the whole?