Question

A dishonest shopkeeper professes to sell sugar at his cost price, but uses a $950g$ for $1kg$. Find his profit percent.

Answer 1

Hint: First given that the shopkeeper sells sugar at his cost price but uses a false weight of $950g$ for $1kg$. The gain percentage can be measured using the formula of the profit percentage Profit $ = $ $(\dfrac{{SP - CP}}{{CP}} \times 100)\% $ where SP is the selling price of the given product and CP is the original cost price of the given sugar.

Complete step by step solution:
Let the cost price of one gram of sugar be one rupee, let us assume that he sells one thousand grams of sugar so the price of $1kg$ sugar will be $Rs.1000$ . Since he sells only $950g$ in the price of $1kg$ we get that the cost price $CP = Rs.950$ and the selling price $SP = Rs.1000$
Thus, using the profit formula, we get Profit $\% $ $ = (\dfrac{{SP - CP}}{{CP}} \times 100)\% $
Substituting the values, we have Profit $\% $ $ = (\dfrac{{1000 - 950}}{{950}} \times 100)\% $ (subtraction which is the minus of given two or more than two numbers, but here comes with the one condition that in subtraction the greater number sign represented in the given number will stay constant example $2 - 3 = - 1$ )
Now using the subtraction operation, we get Profit $\% $ $ = (\dfrac{{50}}{{950}} \times 100)\% $
Now using the multiplication operation, we get Profit $\% $ $ = (\dfrac{{5000}}{{950}})\% $
Now finally using the division we have Profit $\% $ $ = (\dfrac{{500}}{{95}})\% $ $ \Rightarrow $ Profit $ = (\dfrac{{100}}{{19}})\% $ which is divisible by the common number of $5$
Hence, we get the profit percentage as Profit $\% $ $ = (\dfrac{{100}}{{19}})\%=5.26\% $

Note: The profit percentage is the selling price minus the cost price of the given particular product, Profit is incurred through normal business operations. There are three types of profit. Gross profit and operating profit and net profit.
By the division method we have Profit $ = (\dfrac{{500}}{{95}}) \times \dfrac{5}{5}$ multiplied and divide by the number five and hence we get Profit $ = (\dfrac{{100}}{{19}})\% $