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?

Answer 1

Total number of hens bought = 100
C.P of 100 hens = Rs. 8000
$\therefore$ C.P of each hen $=Rs.\frac{8000}{100}=Rs.80$
and C.P of 20 hens $=Rs.80\times 20$
=Rs. 1600
Gain $=5\%$
$\therefore$ S.P of 20 hens $=Rs.\frac{1600\times (100+5)}{100}$
$=Rs.\frac{1600\times 105}{100}$
=Rs. 1680
Gain on the whole $=20\%$
$\therefore$ Total S.P of 100 hens $=Rs.\frac{8000\times (100+20)}{100}$
$=Rs.\frac{8000\times 120}{100}=Rs.9600$
Now C.P of remaining hens = 100 - 20 = 80
$=80\times Rs.80=Rs.6400$
and S.P of remaining hens = Rs. 9600 - 1680
=Rs. 7920
$\therefore$ Total gain = Rs. 7920 - 6400
=Rs. 1520
$Gain\%=\frac{1520\times 100}{6400}=23.75\%$