Question

If goods are purchased for Rs. 450 and 1/3 is sold at a loss of 10%. At what gain percentage should the remainder be sold to have a gain of 20% on the whole transaction?

Answer 1

Hint: In this particular question use the concept that the cost price of the (1/3) goods is equal to the cost price of the whole goods divide by 3 and the selling price of the (1/3) goods = cost price of the (1/3) goods – 10% of cost price of the (1/3) goods so use these concepts to reach the solution of the question.

Complete step-by-step answer:
Given data:
Cost price of the goods = Rs. 450
Cost price of the (1/3) goods = cost price of the whole goods divided by 3.
So, the cost price of the (1/3) goods = (450/3) = 150 Rs.
So the cost price of the remaining goods = 450 – 150 = 300 Rs.
Now it is given that (1/3) of the goods is sold at 10% loss.
So the selling price of the (1/3) goods = cost price of the (1/3) goods – 10% of the cost price of the (1/3) goods.
So the selling price of the (1/3) goods = 150 - $ \left( {\dfrac{{10}}{{100}}} \right)150 $
Therefore, 150 – 15 = 135 Rs.
Now we have to gain overall 20% on the whole transaction.
So the 20% of the Rs. 450 = $ \left( {\dfrac{{20}}{{100}}} \right)450 = 90 $ Rs.
But he has lost Rs. 15 in the first transaction.
So overall he has to sell the remaining goods at a profit of (90 + 15) = 105 Rs.
Cost price of the remaining goods = 300 Rs.
So the selling price of the remainder goods must be = cost price of the remainder goods + overall profit
So the selling price of the remaining goods = 300 + 105 = 405 Rs.
Now the gain percentage is the ratio of the difference of the selling and the cost price to the cost price multiplied by 100.
So the gain percentage = $ \dfrac{{{\text{selling price - cost price}}}}{{{\text{cost price}}}} \times 100 $
So the gain percentage = $ \dfrac{{405 - 300}}{{300}} \times 100 $
So the gain percentage = $ \dfrac{{105}}{{300}} \times 100 = 35 $ %.
So he has to sell the remaining goods at a gain percentage of 35% so that he gets overall 20% profit on the whole transaction.
So this is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that the gain percentage is the ratio of the difference of the selling and the cost price to the cost price multiplied by 100, so first find out the overall profit such that he gains 20 % on the whole transaction as above so the selling price is the sum of the overall profit and the cost price of the remainder of goods then use the above described formula we will get the required answer.