Certainly! Let's solve the given problem step-by-step.
First, we are given the selling price and the profit. We need to find the cost price and the profit percent.
### Finding the Cost Price:
Given:
- Selling Price [tex]\((\text{SP}) = ₹300\)[/tex]
- Profit [tex]\((\text{Profit}) = ₹50\)[/tex]
The formula for calculating the cost price (CP) is:
[tex]\[
\text{Cost Price} = \text{Selling Price} - \text{Profit}
\][/tex]
Substituting the given values:
[tex]\[
\text{Cost Price} = ₹300 - ₹50 = ₹250
\][/tex]
So:
[tex]\[
\text{Cost Price} = ₹250
\][/tex]
### Finding the Profit Percent:
The formula for calculating the profit percent is:
[tex]\[
\text{Profit Percent} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100
\][/tex]
Substituting the values of profit and cost price:
[tex]\[
\text{Profit Percent} = \left( \frac{₹50}{₹250} \right) \times 100
\][/tex]
Simplifying the fraction:
[tex]\[
\text{Profit Percent} = \left( \frac{50}{250} \right) \times 100 = 0.2 \times 100 = 20\%
\][/tex]
Therefore:
[tex]\[
\text{Profit Percent} = 20\%
\][/tex]
### Final Solution:
[tex]\[
\begin{aligned}
\text{Cost price} & = \text{Selling price} - \text{Profit} \\
& = ₹300 - ₹50 \\
& = ₹250
\end{aligned}
\][/tex]
So the cost price of the box is [tex]\(₹250\)[/tex].
[tex]\[
\text{Profit percent} = \left( \frac{\text{Profit}}{\text{Cost price}} \right) \times 100 = \left( \frac{₹50}{₹250} \right) \times 100 = 20\%
\][/tex]
Thus, the profit percent made in this transaction is 20%.
