 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 the percentage profit on the rest of the rice.

Hint: Start by finding the one-third of cost price of rice, using the formula of profit percentage find the value of selling price for the first case, similarly find the selling price for second case as well, subtract the two to get the selling price of two-third of rice, and hence find the value of cost price of two-third of rice, using these values evaluate the profit percentage.

Given, Cost price of rice = Rs. 4,500
Therefore, Cost price of one-third of total rice = $Rs\dfrac{{4500}}{3} = Rs.1500$
Profit of one-third of total rice = 10%
So, $Profit\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100$
$10\% = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100$
$10\% = \dfrac{{S.P. - 1500}}{{1500}} \times 100$
$S.P. - 1500 = 150$
$S.P. = Rs.1650$
Hence, selling price of one-third of total rice = Rs.1650
Now, profit on the whole % $= \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100$
$12 = \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100$
$12 = \dfrac{{S.P. - 4500}}{{4500}} \times 100$
$S.P. - 4500 = 540$
$S.P. = Rs.5040$
Thus, selling price of the two-thirds of rice = Rs. 5,040 – Rs. 1,650 = Rs. 3,390
Cost price of two-third of rice will be = Rs. 4,500 – Rs. 1500 = Rs. 3000
%profit on the rest of rice$= \dfrac{{S.P. - C.P.}}{{C.P.}} \times 100 = \dfrac{{3390 - 3000}}{{3000}} \times 100 = 13\%$
Therefore, Percentage profit on the rest of the rice is $13\%$

Note: In the question, they have asked to find the profit percentage when the shopkeeper desires 12% on the whole and they have provided us with a profit percent of one-third of rice, so make sure while calculating you take correct ratios.