Sure, let's find the cost price (CP) of the toy step-by-step.
1. Understanding the Problem:
- Selling Price (SP) of the toy is ₹25.
- Gain (or profit) is 25%.
- We need to find the Cost Price (CP) of the toy.
2. Relation Between SP, CP, and Gain:
- Gain is calculated as a percentage of the Cost Price (CP).
- The gain percentage is given by [tex]\(\text{Gain Percent} = \left( \frac{\text{Gain}}{\text{CP}} \right) \times 100 \)[/tex].
3. Expressing Gain:
- Gain = Selling Price (SP) - Cost Price (CP).
4. Setting Up the Equation:
- Given that the gain percentage is 25%, we have:
[tex]\[
\text{Gain} = \frac{25}{100} \times \text{CP} = 0.25 \times \text{CP}
\][/tex]
5. Incorporating the Selling Price:
- Since Gain = SP - CP, we can write:
[tex]\[
0.25 \times \text{CP} = 25 - \text{CP}
\][/tex]
6. Solving for CP:
- Rearrange the above equation to isolate CP:
[tex]\[
0.25 \times \text{CP} + \text{CP} = 25
\][/tex]
[tex]\[
1.25 \times \text{CP} = 25
\][/tex]
[tex]\[
\text{CP} = \frac{25}{1.25}
\][/tex]
[tex]\[
\text{CP} = 20
\][/tex]
So, the Cost Price (CP) of the toy is ₹20.
