Great! Let's proceed step-by-step to solve the problem of finding the selling price given the cost price and the percentage gain.
1. Understand the Variables:
- Cost Price (C.P.): Rs 9600
- Gain Percentage: [tex]\( 16 \frac{2}{3} \% \)[/tex]
2. Convert the mixed fraction to a decimal:
- Gain Percentage: [tex]\( 16 \frac{2}{3} \% \)[/tex] can be converted to a decimal. As a fraction, it is [tex]\( 16 + \frac{2}{3} \% \)[/tex].
- Converting this, we get [tex]\( 16.66666666666667\% \)[/tex].
3. Calculate the Total Percentage:
- The selling price is based on the cost price increased by the gain percentage.
- Total Percentage = 100% (original cost) + Gain Percentage = 100% + 16.66666666666667% = 116.66666666666667%.
4. Calculate the Selling Price:
- The selling price (S.P.) is calculated by applying this total percentage to the cost price.
- Formula: [tex]\(S.P. = \frac{\text{Total Percentage}}{100} \times \text{Cost Price}\)[/tex]
- Plugging in the numbers: [tex]\(S.P. = \frac{116.66666666666667}{100} \times 9600\)[/tex]
5. Calculate the Result:
- By performing the multiplication, we find: [tex]\( S.P. = 116.66666666666667 / 100 \times 9600 = 1.16666666666667 \times 9600 = 11200.0 \)[/tex]
Thus, the steps show that starting with a cost price of Rs 9600 and a gain of [tex]\( 16 \frac{2}{3} \% \)[/tex], the selling price is Rs 11200.
