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# A shopkeeper professes to sell his goods at cost price but uses a weight of $800$ grams instead of a kilogram weight. Thus, he makes a gain of:A. $10\%$B. $15\%$C. $20\%$D. $25\%$

Last updated date: 20th Jun 2024
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Hint: Here we will be using the formula of gain percentage i.e. ${\text{Gain}}\% = \dfrac{{{\text{Gain}}}}{{{\text{Original weight}}}} \times 100$ , where the gain is the difference between the original weight and the new weight.

Step 1: As we know that one kilogram equals
$1000$ grams. The actual weight used by the shopkeeper is
$800$ grams so we will be calculating the gain by subtracting the original weight from the new/actual weight as shown below:
${\text{Gain = 1000 - 800}}$
By doing the subtraction in the RHS side of the above expression we get:
$\Rightarrow {\text{Gain = 200}}$
Step 2: We will be using the formula ${\text{Gain}}\% = \dfrac{{{\text{Gain}}}}{{{\text{Original weight}}}} \times 100$ to calculate the gain percentage by substituting the values of
${\text{Gain = 200}}$ and
${\text{Original weight = 800}}$ as calculated below:
$\Rightarrow {\text{Gain}}\% = \dfrac{{200}}{{800}} \times 100$
By solving the division in the RHS side of the above expression we get:
$\Rightarrow {\text{Gain}}\% = \dfrac{{100}}{4}$
By doing the final division in the above expression we get:
$\Rightarrow {\text{Gain}}\% = 25\%$

Option D is correct.

Note:
Students need to take care while solving these types of questions that the amount of discount which is given on the marked price equals to as below:
$\dfrac{{{\text{Discount }}\% }}{{100}} \times {\text{M}}{\text{.P}}$, and we will be subtracting this value from the marked price for calculating the value of the selling price.
Also, you should remember which one is the original weight and which one is new for calculating the value of gain.