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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
\[\text { C . P of 100 hens = Rs } . 8000\]
\[\text { Cost of one hen = } \frac{8000}{100} =\text { Rs } . 80 \]
\[\text { C . P of 20 hens = Rs } . ( 80 \times 20) = Rs . 1600\]
\[\text { Gain % = 5 % }\]
\[\text { S . P = C } . P\left( \frac{100 + \text { gain % }}{100} \right)\]
\[\text { S . P }= 1600 \times \frac{105}{100} = Rs . 1680\]
\[\text { C . P of 80 hens = Rs } . (80 \times 80) = \text { Rs }. 6400\]
\[\text { Gain on 80 hens = S . P of 80 hens - C . P of 80 hens } \]
\[\text { Gain on 100 hens = Gain on 80 hens + Gain on 20 hens }\]
\[\text { Gain on 100 hens = Rs . (80 + S . P of 80 hens - } 6400)\]
\[\text { Gain % on 100 hens } = \frac{\text { Gain on 100 hens }}{\text { C . P of 100 hens }} \times 100\]
\[20 = \frac{(80 + \text { S . P of 80 hens } - 6400)}{8000} \times 100\]
\[1600 = 80+\text { S.Pof 80 hens-6400 S.P of80 hens= Rs }.(1600+6400-80) \text { S.P of}\text { 80 hens=Rs.7920 \text { Gain on 80 hens=S.P of 80 hens-C.P } of 80 hens=Rs }.(7920-6400)=Rs.1520\text { Gain % on 80 hens= }\frac{Gain on 80 hens}{C . P of 80 hens}\times100=\frac{1520}{6400}\times100=23.75%\text { Therefore,Toshibagained23.75%on80hens }.\]
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