Question

Mahesh bought 100 kg of rice for Rs. 1040 and sold it at a loss of as much money as he received for 30 kg rice. At what price did he sell the rice?

Answer 1

Hint: Mahesh suffered loss after selling the rice he bought before. Cost price of 100 kg of rice is Rs. 1040. Let the selling price of rice per kg be Rs. X, then the selling price of all the 100 kgs of rice will be Rs. $ 100X $ . Subtract this selling price of 100 kg from the cost price to get the loss. And we are also given that this loss is equal to the money he received for 30 kg rice; for 30 kg the selling price is $ 30X $ . Equate the loss with $ 30X $ to get the selling price of each kg.

Complete step-by-step answer:
We are given that Mahesh bought 100 kg of rice for Rs. 1040 and sold it at a loss of as much money as he received for 30 kg rice.
We have to find at what price he sold the rice.
Cost price of 100 kg is Rs. 1040.
Let the selling price of 1 kg rice be X, this gives the selling price of 100 kg as Rs. $ 100X $ .
Loss is Cost price of 100kg minus selling price of 100kg, which is $ 1040 - 100X $
And given that this loss is equal to selling price of 30 kg, SP of 30 kg is $ 30X $
 $ \Rightarrow 1040 - 100X = 30X $
 $ \Rightarrow 30X = 1040 - 100X $
Sending $ 100X $ to the LHS, we get
 $ \Rightarrow 30X + 100X = 130X = 1040 $
 $ \therefore X = \dfrac{{1040}}{{130}} = 8 $
Therefore, the selling price of 1 kg of rice is Rs. 8 and 100 kg of rice is Rs. 800.
So, the correct answer is “800”.

Note: When a person suffers a loss, the cost price is greater than the selling price whereas for a profit the cost price is less than the selling price. So to find loss we subtract SP from CP as CP is larger and in profit, we subtract CP from SP as SP is larger.