Question

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) \[25\% \]

Answer 1

Hint:
Here, we will find the gain percentage using the formula \[{\text{Gain}}\% = \dfrac{{{\text{Gain}}}}{{{\text{Original Weight}}}} \times 100\] from the given values, where Gain the difference of the original weight and the new weight that the shopkeeper used.

Complete step by step solution:
We are given that a shopkeeper professes to sell his goods at cost price but uses a weight of 800 grams instead of a kilogram weight.
We know that a kilogram has a 100 g.
So, we will subtract the 800 grams from the 1000 grams to find the gain in weight, we get
\[
  {\text{Gain}} = 1000 - 800 \\
   = {\text{2}}00{\text{ g}} \\
 \]
We know that the formula to calculate the gain percentage is calculated as \[{\text{Gain}}\% = \dfrac{{{\text{Gain}}}}{{{\text{Original Weight}}}} \times 100\].
Substituting the values of gain and original weight in the above formula for gain percentage of the given article, we get
\[
  {\text{Gain}}\% = \dfrac{{200}}{{800}} \times 100 \\
   = \dfrac{2}{8} \times 100 \\
   = 25\% \\
 \]

Thus, we get that the gain percentage is \[25\% \].

Note:
While solving these types of problems, the amount of discount given on the marked price is \[\dfrac{{{\text{Discount Percentage}}}}{{100}} \times {\text{Marked Price}}\] and then this amount is subtracted from the market price in order to get the selling price. In this question, students must note that we have added all the expenses of transportation and travelling while finding the cost price of an article. So this point must be taken care of.