Sure thing! Let's solve each part step-by-step.
### (a) When the Cost Price (CP) is Rs 1,540 and there is a 5% loss:
1. Determine the loss amount:
- Loss percentage = 5%
- Cost Price (CP) = Rs 1,540
[tex]\[
\text{Loss Amount} = \left( \frac{\text{Loss Percentage}}{100} \right) \times \text{CP}
\][/tex]
[tex]\[
\text{Loss Amount} = \left( \frac{5}{100} \right) \times 1540 = 77
\][/tex]
2. Calculate the Selling Price (SP):
[tex]\[
\text{SP} = \text{CP} - \text{Loss Amount}
\][/tex]
[tex]\[
\text{SP} = 1540 - 77 = 1463
\][/tex]
Therefore, the Selling Price (SP) when the CP is Rs 1,540 and the loss is 5% is Rs 1,463.
### (b) When the Cost Price (CP) is Rs 760 and there is a 3 [tex]\(\frac{1}{8}\)[/tex]% loss:
1. Convert the mixed number to a fraction:
- Mixed Number: [tex]\( 3 \frac{1}{8} \)[/tex]
- Convert: [tex]\( 3 \frac{1}{8} = 3 + \frac{1}{8} = \frac{24}{8} + \frac{1}{8} = \frac{25}{8} \)[/tex]
2. Determine the loss amount:
- Loss percentage = [tex]\(\frac{25}{8} \%)
- Cost Price (CP) = Rs 760
\[
\text{Loss Amount} = \left( \frac{\text{Loss Percentage}}{100} \right) \times \text{CP}
\]
\[
\text{Loss Amount} = \left( \frac{25}{8 \times 100} \right) \times 760 = \left( \frac{25}{800} \right) \times 760 = 23.75
\]
3. Calculate the Selling Price (SP):
\[
\text{SP} = \text{CP} - \text{Loss Amount}
\]
\[
\text{SP} = 760 - 23.75 = 736.25
\]
Therefore, the Selling Price (SP) when the CP is Rs 760 and the loss is 3 \(\frac{1}{8}\)[/tex]% is Rs 736.25.
### Summary:
- In case (a), the SP is Rs 1,463.
- In case (b), the SP is Rs 736.25.
