To find the Cost Price (CP) when given the Selling Price (SP) and the percentage loss, we use the formula relating SP, CP, and loss percentage. The formula for calculating CP when there is a loss is:
[tex]\[ CP = \frac{SP}{1 - \left(\frac{\text{Loss\%}}{100}\right)} \][/tex]
Let's solve each part step-by-step:
### Part (a)
Given:
- Selling Price ([tex]\(SP_a\)[/tex]) = Rs 851
- Loss ([tex]\(\%\)[/tex]) = 8%
Using the formula:
[tex]\[ CP_a = \frac{SP_a}{1 - \left(\frac{8}{100}\right)} \][/tex]
[tex]\[ CP_a = \frac{851}{1 - 0.08} \][/tex]
[tex]\[ CP_a = \frac{851}{0.92} \][/tex]
[tex]\[ CP_a \approx 925 \][/tex]
So, the cost price when the SP is Rs 851 with an 8% loss is approximately Rs 925.
### Part (b)
Given:
- Selling Price ([tex]\(SP_b\)[/tex]) = Rs 560
- Loss ([tex]\(\%\)[/tex]) = [tex]\(6\frac{2}{2}\%\)[/tex]
First, we convert [tex]\(6\frac{2}{2}\%\)[/tex] to a decimal. [tex]\(6\frac{2}{2}\%\)[/tex] is equivalent to [tex]\(6.5\%\)[/tex].
Using the formula:
[tex]\[ CP_b = \frac{SP_b}{1 - \left(\frac{6.5}{100}\right)} \][/tex]
[tex]\[ CP_b = \frac{560}{1 - 0.065} \][/tex]
[tex]\[ CP_b = \frac{560}{0.935} \][/tex]
[tex]\[ CP_b \approx 598.93 \][/tex]
So, the cost price when the SP is Rs 560 with a [tex]\(6.5\%\)[/tex] (or [tex]\(6\frac{2}{2}\%\)[/tex]) loss is approximately Rs 598.93.
### Summary
- For SP = Rs 851 with 8% loss, CP ≈ Rs 925
- For SP = Rs 560 with [tex]\(6\frac{2}{2}\%\)[/tex] loss, CP ≈ Rs 598.93
