Alright, let's solve the problem step-by-step.
1. Understand the given information:
- Selling Price (SP) = ₹810
- Gain Percent (G%) = 8%
2. Use the relationship between Cost Price (CP), Selling Price (SP), and Gain Percent (G%):
The formula connecting these quantities is:
[tex]\[
\text{Selling Price} = \text{Cost Price} + \text{Gain}
\][/tex]
where Gain is given by:
[tex]\[
\text{Gain} = \frac{\text{Cost Price} \times \text{Gain Percent}}{100}
\][/tex]
3. Substitute Gain into the Selling Price formula:
[tex]\[
\text{Selling Price} = \text{Cost Price} + \frac{\text{Cost Price} \times \text{Gain Percent}}{100}
\][/tex]
4. Factor out the Cost Price (CP):
[tex]\[
\text{Selling Price} = \text{Cost Price} \times \left(1 + \frac{\text{Gain Percent}}{100}\right)
\][/tex]
5. Rearrange the formula to solve for Cost Price (CP):
[tex]\[
\text{Cost Price} = \frac{\text{Selling Price}}{1 + \frac{\text{Gain Percent}}{100}}
\][/tex]
6. Insert the given values (SP = ₹810 and G% = 8%):
[tex]\[
\text{Cost Price} = \frac{810}{1 + \frac{8}{100}}
\][/tex]
7. Simplify the denominator:
[tex]\[
\text{Cost Price} = \frac{810}{1 + 0.08}
\][/tex]
[tex]\[
\text{Cost Price} = \frac{810}{1.08}
\][/tex]
8. Calculate the Cost Price:
[tex]\[
\text{Cost Price} = 750
\][/tex]
So, Sam should have paid ₹750 for the Jan.
