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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?

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28.45%

21.41%

29.72%

23.75%

answer is C.

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Detailed Solution

Given,
Cost price (CP) of 100 hens = Rs.8000.
CP of 1 hen =Rs.80.

SP = CP 100 + gain % 100

CP of 20 hens is Rs.80×20 =1600Rs.

Gain % = 5 % SP = CP 100 + gain % 100 ⇒ 1600105100 ⇒ 1680 CP of 80 hens is Rs .80 (80) = R s .6400

Gain on 80 hens = SP of 80 hens - CP of 80 hens
Gain on 100 hens = gain on 80 hens + gain on 20 hens

Gain on 100 hens = 80 + SP of 80 hens − 6400

Gain % on 100 hens = gain on 100 hens CP of 100 hens (100) 20 = 80 + SP of 80 hens − 6400 8000 (100) SP of 80 hens = 7920

Now,

Gain on 80 hens = SP of 80 hens − CP of 80 hens ⇒ 7920 − 6400 ⇒ 1520

Now,

G a i n % on 80 hens = Gain on 80 hens CP of 80 hens (100) ⇒ 15206400 (100) ⇒ 23.75 %

Therefore, Toshiba gained 23.75% on 80 hens.
Therefore, option (3) is correct.

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