Certainly! Let's solve each part step-by-step.
### Part (a): Selling Price (SP) = Rs 924, Gain = 10%
To find the Cost Price (CP), we use the formula that relates selling price (SP), cost price (CP), and gain percentage:
[tex]\[ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Gain Percentage}}{100}} \][/tex]
Given:
- SP = Rs 924
- Gain Percentage = 10%
Substitute the values into the formula:
[tex]\[ \text{CP} = \frac{924}{1 + \frac{10}{100}} \][/tex]
[tex]\[ \text{CP} = \frac{924}{1 + 0.10} \][/tex]
[tex]\[ \text{CP} = \frac{924}{1.10} \][/tex]
Now, divide 924 by 1.10:
[tex]\[ \text{CP} \approx 839.9999999999999 \][/tex]
So, the Cost Price (CP) for part (a) is approximately Rs 840 (considering a rounding to the nearest whole number, it is Rs 840).
### Part (b): Selling Price (SP) = Rs 1,755, Gain = 12.5%
To find the Cost Price (CP), again we use the same formula:
[tex]\[ \text{CP} = \frac{\text{SP}}{1 + \frac{\text{Gain Percentage}}{100}} \][/tex]
Given:
- SP = Rs 1,755
- Gain Percentage = 12.5%
Substitute the values into the formula:
[tex]\[ \text{CP} = \frac{1755}{1 + \frac{12.5}{100}} \][/tex]
[tex]\[ \text{CP} = \frac{1755}{1 + 0.125} \][/tex]
[tex]\[ \text{CP} = \frac{1755}{1.125} \][/tex]
Now, divide 1755 by 1.125:
[tex]\[ \text{CP} = 1560 \][/tex]
So, the Cost Price (CP) for part (b) is Rs 1560.
### Summary:
- For (a), the CP is approximately Rs 840.
- For (b), the CP is Rs 1560.
