Question

Irshad bought 100 hens for Rs.8000 and sold 20 of these at a gain of 5%. At wh
b
percent must be sell the remaining hens so as to gain 20% on the whole?​

Answer 1

Given, Total hens = 100 Remaining hens = 100-20 = 80 hens Irshad bought 100 hens for = Rs 8000 1 hen cost is = 8000/100 = Rs 80 20 hens cost = 20 × 80 = Rs 1600 Given, Gain = 5% SP = 105/100 × 1600 = Rs 1680 CP for 80 hens = 80 × 80 = Rs 6400 SP of 80 hens = Rs (1600 + 6400-80) = Rs 7920 Gain on 80 hens = SP of 80 hens – CP of 80 hens = 7920 – 6400 = Rs 1520 Gain % = (gain/cost price) × 100 Gain% on 80 hens = (1520/6400) × 100 = 23.75% ∴ irshad require 23.75% gain on the remaining hens (80 hens).

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Answer 2

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C.P. of 100 hens = ₹8000 ,

Gain = 20%

S.P. of 100 hens$= \frac{(100 + Profit\%)}{100} \times C.P.$

$=₹\frac{(100 + 20)}{100}\times 8000 = \frac₹{120}{100}\times8000 = ₹9600$

C.P. of 100 hens$=₹8000$

•°• C.P. of 20 hens$= ₹ \frac{8000}{100} \times 20 =₹1600.$

Gain = 5%

•°• S.P. of 20 hens$=\frac{(100 + 5)}{100}\times 1600 = ₹\frac{105}{100}\times 1600 = ₹1680$

•°• S.P. of 80 hens = S.P. of 100 hens - S.P. of 20 hens

:⟹ ₹ 9600 - ₹ 1680 = ₹ 7920.

•°• C.P. of 80 hens = C.P. of 100 hens - C.P. of 20 hens

:⟹ ₹ 8000 - ₹ 1600 = ₹ 6400.

•°• Gain = ₹ 7920 - ₹ 6400 = ₹ 1520

•°• Gain$%=\frac{Total~gain}{C.P.}\times 100 = \frac{1520}{6400}\times 100$

$= \frac{94}{4}\% =23 \frac{3}{4}\% = 23.75\%.$

Hence, he should sell the remaining hens at a gain of 23 75%