Question

A shopkeeper bought rice worth Rs. 4,500. He sold one-third of it at 10% profit. If he desires a profit of 12% on the whole; find : (i) the selling price of the rest of the rice. (ii) the percentage profit on the rest of the rice.

Answer 1

C.P of the rice = Rs. 4500
Profit desired on the whole = 12%
$\therefore$ S.P. of the whole rice = $\frac{(100+gain}{100}\times C.P.$
= $\frac{(100+12)}{100}\times Rs.4500=Rs.\frac{112}{100}\times 4500$
= 112 $\times$ 45 = Rs. 5040
C.P. of $\frac{1}{3}ofrice=\frac{1}{3}\times Rs.4500$
= Rs. 1500
Since, gain on $\frac{1}{3}$ of rice = 10%
$\therefore$ S.P. on it = $\left(\frac{100+gain}{100}\right)\times C.P.$
= $\frac{100+10}{100}\times Rs.1500=Rs.\frac{110}{100}\times 1500$
= 11 $\times$ 150 = Rs. 1650
Remaining C.P. of the rice
= Rs. 4500 - Rs.1500 = Rs.3000
Remaining S.P. of the rice
= Rs. 5040 - Rs. 1650 = Rs. 3390
Profit on the remaining rice
= Rs. 3390 - Rs. 3000 = Rs.390
Gain % on the remaining rice = $\frac{390}{3000}\times 100$
= $\frac{390\times 100}{3000}=13$%
$\therefore$ (i) S.P. of the rest of the price = Rs. 3390
(ii) % profit on the rest of the rice = 13%