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# A fair price shopkeeper takes 10 percent profit on his goods. He lost 20 percent goods during theft. What is his loss percentage?

Last updated date: 29th Feb 2024
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Hint: Now first let us assume that the shopkeeper had 100 goods and the cost price of each item is 10Rs. Now we will first find the selling price of each item. Now we know that there was a loss of 20 percent goods. Hence we will calculate the remaining number of goods. Now we know the selling price of each item hence we will calculate the total selling price of the goods after loss.
Now we will calculate loss by formula loss = CP – SP.

Now to solve this question let us say that the shopkeeper has 100 goods. The cost price of each item be 1Rs.
Now the total cost price of his goods will be Rs 100.
Now we know that the shopkeeper makes 10 percent profit on goods.
Now we know that the profit percentage is $\dfrac{\text{profit}}{\text{costprice}}\times 100$ .
Hence we have, $10=\dfrac{\text{profit}}{100}\times 100$
Hence the profit is Rs 10.
Hence the selling price of goods will be 100 + 10 = Rs 110.
Also since there are 100 goods the SP of each item is Rs 1.1.
Now we are given that after a theft the loss was 20 percent goods.
Now again we know that loss percent = $\dfrac{\text{loss}}{\text{cost price}}\times 100$
Hence we get, $20=\dfrac{loss}{100}\times 100$
Hence we get the loss of 20 goods.
Now remaining goods = 80.
SP of 80 goods will be $\left( 80\times 1.1 \right)=88$ .
Hence the total selling price of 80 goods will be 88 Rs.
Now the Cost price was 100 Rs and now after loss the selling price is 88 Rs.
Hence the loss is 12 Rs.
Hence the loss percentage is $\dfrac{12}{100}\times 100=12$.
Hence there is a loss of 12 percent.

Note: Now note that we cannot add the percentage together if there is a profit of 10 percent and then loss of 10 percent it does not mean the loss is 20 – 10 = 10. We will have to assume the cost price and number of goods to solve such problems. Also note that the cost price and number of goods can be any number but for simple calculations we have taken the values as 1 and 100 Rs.