Question

A trader marks his goods \[30\% \] above the cost price but makes a reduction of cost price \[6\dfrac{1}{4}\% \] on the market price for ready money. His gain percent is:
A. \[23.75\% \]
B. \[23.25\% \]
C. \[21.875\% \]
D. \[20\% \]

Answer 1

Hint: In order to solve the above question, we will use a few formulas to calculate the amount of selling price and the cost price of the goods. After finding these two values, we will use them in another formula to find the gain percent. This will give us the final answer. To find all this, you will have to assume the value of the cost price first.

Formula used:
The formula that we will be using to find the solutions are:
\[{\text{gain percentage = }}\dfrac{{{\text{selling price }} - {\text{ cost price}}}}{{{\text{cost price}}}} \times 100\] .

Complete step by step solution:
We are given that a trader marks his goods \[30\% \] above the cost price.
In the first step, we will assume that the cost price of the item is equal to \[100\] .
Now, we will calculate the price displayed by the shopkeeper.
MRP by the shopkeeper \[ = {\text{ cost price }} \times {\text{ percentage by which goods were marked up}}\]
 \[
   = 100 + \dfrac{{30}}{{100}} \times 100 \\
   = 130 \\
 \] .
This gives us MRP \[ = 130\] .
Now, we have to find the selling price of the item.
For this, we are given that the shopkeeper makes a reduction of cost price \[6\dfrac{1}{4}\% \] on the market price for ready money.
So,
The selling price of the item \[ = {\text{ market price (MRP) }} - {\text{ }}\left( {{\text{market price }} \times {\text{ discount on MRP}}} \right)\] .
  \[
 = 130 - \dfrac{{25}}{{400}} \\
 = 121.875 \\
 \] .
Therefore, the Selling price \[ = 121.875\] .
Now, we have to find the gain percent.
We will use the formula mentioned above.
\[{\text{gain percentage = }}\dfrac{{{\text{selling price }} - {\text{ cost price}}}}{{{\text{cost price}}}} \times 100\]
\[
   = \dfrac{{121.875 - 100}}{{100}} \times 100 \\
   = 21.875 \\
 \] .
So, the correct answer is Option C.

Note: While solving questions similar to the one given above, always assume the cost to be either \[x\] or \[100\] . This makes the question easier and simpler to solve. Always remember the formulas used to calculate cost price, selling price, gain percent and loss percent. You can easily solve the sums with the help of these formulas.