Toshiba bought 100 hens for Rs 8000 and sold 20 of these at a gain of 5%.
Question:

Toshiba bought 100 hens for Rs 8000 and sold 20 of these at a gain of 5%. At what gain percent she must sell the remaining hens so as to gain 20% on the whole?

Solution:

C.P of 100 hens $=$ Rs. 8000

Cost of one hen $=\frac{8000}{100}=$ Rs. 80

C.P of 20 hens $=$ Rs. $(80 \times 20)=$ Rs. 1600

Gain $\%=5 \%$

$S . P=C . P\left(\frac{100+g \text { ain } \%}{100}\right)$

$S \cdot P=1600 \times \frac{105}{100}=$ Rs. 1680

$C . P$ of 80 hens $=$ Rs. $(80 \times 80)=$ Rs. 6400

Gain on 80 hens $=S . P$ of 80 hens $-C . P$ of 80 hens

Gain on 100 hens = Gain on 80 hens + Gain on 20 hens

Gain on 100 hens $=$ Rs. $(80+S \cdot P$ of 80 hens $-6400)$

Gain $\%$ on 100 hens $=\frac{\text { Gain on } 100 \text { hens }}{C . P \text { of } 100 \text { hens }} \times 100$

$20=\frac{(80+S . P \text { of } 80 \text { hens }-6400)}{8000} \times 100$

$1600=80+S . P$ of 80 hens $-6400 S . P$ of 80 hens $=$ Rs. $(1600+6400-80) S . P$ of 80 hens $=$ Rs. 7920 Gain on 80 hens $=S . P$ of 80 hens $-C . P$ of 80 hens $=$ Rs. $(7920-6400)=$ Rs. 1520 Gain $\%$ on 80 hens $=\frac{\text { Gain on } 80 \text { hens }}{C . P \text { of } 80 \text { hens }}$ $\times 100=\frac{1520}{6400} \times 100=23.75 \%$ Therefore, Toshiba gai ned $23.75 \%$ on 80 hens

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