Question

A trader mixes 26 kg of rice at Rs.20 per kg with 30 kg of rice of other variety at Rs.36 per kg and sells the mixture at Rs.30 per kg. What is his profit percent?

Answer 1

Hint: Calculate the cost price and selling price of the rice with the help of the given weight of the rice and rate of them. Now, find profit using the relation: - Profit = S.P. – C.P. and profit percent can be calculated by the relation
$\text{Profit percent = }\dfrac{\text{Profit amount}}{\text{cost price}}\times 100$

Complete step-by-step answer:
Here, the trader is mixing two different types of rice. He mixes 26 kg of one rice which cost is 20 Rs. per kg and 30 kg rice which cost is 36 Rs per kg and hence we need to determine the percentage profit of he sells the mixture at 30 Rs. per kg.
As we know that after mixing the varieties of rice, the weight of the mixture will become the sum of weight of rice. So, we get
Weight of the mixture $=\ 26+30$
$=\ 56\ \text{kg}$
Now, we know the profit in percentage can be given by the relation: -
$\%$Profit=$\dfrac{\text{Profit amount}}{\text{cost price}}\times 100$ …………………………………………………………………(i)
And Profit amount = S.P. – C.P. ………………………………………………………………………(ii)
Where, S.P. stands for selling price
               C.P. stands for cost price
Hence, we need to calculate S.P. and C.P. of the rice and hence the percentage profit.
So, it is given that the cost of rice can be given by adding the costs of both the rice.
As we know, amounts of rice are 26 kg and 30 kg with rates of 20 Rs. per kg and 36 Rs. per kg respectively.
So, total price of the rice $=\ 26\times 20+30\times 36$
$=\ 520+1080$
$=\ 1600\ \text{Rs}$
So, the total price of the rice is 1600 Rs.
Now, we know the trader is selling the whole amount of rice after mixing both the rice at 30 Rs. per kg and amount of mixture is 56 kg.
So, selling price of rice $=\ 56\times 30$
$=\ 1680\ \text{Rs}$.
So, the profit amount can be calculated with the help of equation (ii). Hence, we get
Profit Amount = S.P. – C.P.
$=\ 1680\ -1600$
$=\ 80\ \text{Rs}$
Hence, we can calculate percentage profit using the equation (i) as
$%\ \text{Profit = }\dfrac{\text{Profit amount}}{\text{C}\text{.P}\text{.}}\times 100$
$\text{= }\dfrac{80}{1600}\times 100$
$\text{= }\dfrac{80}{16}=5%$
Hence, profit percent for the given trading process is 5%.

Note: One may go wrong if he/she was formula of profit % as $\dfrac{\text{Profit amount}}{\text{S}\text{.P}\text{.}}\times 100$ which is wrong. So, we need to divide the profit amount by the C.P. not by S.P., it is general mistakes done by the students. So, don’t confuse it with it as well. Weight of the mixture of both the rice is the sum of weight of both the rice. One may get confused here as well.