1. If the cost price is 95% of the selling price, what is the profit percent ?4% 4.75% 5% 5.26%

1. Break Down the Problem

Let's denote the selling price (SP) as $SP$ and the cost price (CP) as $CP$. According to the problem, the cost price is 95% of the selling price, which can be expressed mathematically as: $CP = 0.95 \times SP$ The profit can be calculated using the formula: $\text{Profit} = SP - CP$ The profit percentage is calculated as: $\text{Profit Percent} = \left( \frac{\text{Profit}}{CP} \right) \times 100$

2. Relevant Concepts

From the earlier expressions, we will substitute $CP$ in place of $SP$ to calculate the profit and subsequently the profit percentage.

3. Analysis and Detail

1. Substitute $CP = 0.95 \times SP$ into the profit formula: $\text{Profit} = SP - CP = SP - 0.95 \times SP = 0.05 \times SP$
2. Now calculate the profit percentage using $CP$: $\text{Profit Percent} = \left( \frac{0.05 \times SP}{0.95 \times SP} \right) \times 100$
   • Here $SP$ cancels out: $\text{Profit Percent} = \left( \frac{0.05}{0.95} \right) \times 100$
3. Calculate $\frac{0.05}{0.95}$: $\frac{0.05}{0.95} \approx 0.05263$
4. Now multiply this result by 100 to get the percentage: $\text{Profit Percent} \approx 0.05263 \times 100 \approx 5.26\%$

4. Verify and Summarize

We confirmed the calculations, and the profit percentage is around $5.26\%$.

Final Answer

The profit percent is $5.26\%$.