Question

A Shopkeeper bought wheat for Rs. 35000. Due to leakage in the godown \[\dfrac{1}{7}th\] of the total wheat was spoiled. He sold good wheat at a gain of 10% and the spoiled wheat at a loss of 25%. Find his total gain or loss percent.

Answer 1

Hint: We start solving the problem by calculating the cost price of the good wheat and spoiled wheat. We then find the selling price of spoiled wheat first using the loss percentage given in the problem. Similarly, we find the selling price of good wheat using the gain percentage given in the problem. We then add both the selling prices of both good wheat and spoiled wheat to get the selling price of all the wheat the shop keeper just bought. We subtract the final selling price from the cost price given initially to get the total gain/loss. Using this we find the required percentage.

Complete step by step answer:
In the question we are given a shopkeeper or bought wheat for Rs. 35000. Now, due to leakage $\dfrac{1}{7}$ of the total wheat is spoiled. Now, he sold the good wheat at 10% gain and the bad wheat at 25% loss. We need to find the total gain/loss percent.
According to the problem, the total cost of wheat is Rs. 35000.
Now, let us find the cost price of the spoiled wheat.
So, the cost of spoiled wheat is $\dfrac{1}{7}\times Rs35000$ which is equal to Rs. 5000.
Hence, the cost price of spoiled wheat is Rs 5000.
As we know that the spoiled wheat was sold at 25% loss, so we can say that if the cost price is considered as 100% so the selling price is considered as $\left( 100-25 \right)\%$ or 75%.
So, we got the selling price of spoiled wheat is $\dfrac{75}{100}\times 5000=Rs3750$
So, the cost price of spoiled wheat is Rs.5000 and selling price of spoiled wheat is Rs.3750.
Now, let us find the cost price of the good wheat.
Now, we will consider the good quality of wheat whose cost price is $Rs\left( 35000-5000 \right)$ which is Rs. 30000.
Hence, the cost price is Rs. 30000.
As we know good quality wheat was sold at 10% gain so we can say that, if the cost price is 100% then the selling price will be $\left( 100+10 \right)\%$ or 110% .
 Hence, the selling price of good quality wheat is $\dfrac{110}{100}\times Rs30000$ which is Rs. 33000.
So, the cost price of good quality wheat is Rs. 30000 and selling price is Rs. 33000.
Let us find the total selling price of the wheat that the shopkeeper bought.
Now the total selling price of the wheat is $Rs.3750+Rs.30000=Rs.36750$.
Let us now find the total profit/loss incurred to the shopkeeper.
Hence Profit $=$ Total selling price $-$ Total cost price
So, profit $=Rs.36750-Rs.35000$
$=Rs.1750$
We know that $\text{profit }\!\!\%\!\!\text{ =}\dfrac{\text{profit}}{\text{cost price}}\times 100\%$.
$=\dfrac{1750}{35000}\times 100\%$.
$=5\%$.
So, total profit is 5%.

Note:
We should calculate profit or loss with respect to the cost price of the commodity. We should not make calculation mistakes while solving this problem. Whenever we get these types of problems, we first try to solve them separately and then add them together in the end to get the result. Similarly, we can also expect problems to find the selling price if the shopkeeper sold all the wheat with a profit percentage of 10%.