In terms of percentage profit, which is the best transaction?
`{:("C.P"("in Rs"),"Profit"("in Rs")),(("I")36,17),(("ii")50,24),(("iii")40,19),(("iv")60,29):}`

Options

A. I
B. II
C. III
D. IV

Answer

To determine which transaction has the best percentage profit, we will calculate the percentage profit for each transaction using the formula:

\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{\text{C.P}} \right) \times 100 \]

where C.P is the cost price and Profit is the profit made on that transaction.

### Step-by-Step Solution:

1. **Transaction I:**
- Cost Price (C.P) = Rs 36
- Profit = Rs 17
- Percentage Profit (P1) = \(\left( \frac{17}{36} \right) \times 100\)
- Calculation:
\[ P1 = \left( \frac{17}{36} \right) \times 100 = \frac{1700}{36} \approx 47.22\% \]

2. **Transaction II:**
- Cost Price (C.P) = Rs 50
- Profit = Rs 24
- Percentage Profit (P2) = \(\left( \frac{24}{50} \right) \times 100\)
- Calculation:
\[ P2 = \left( \frac{24}{50} \right) \times 100 = \frac{2400}{50} = 48\% \]

3. **Transaction III:**
- Cost Price (C.P) = Rs 40
- Profit = Rs 19
- Percentage Profit (P3) = \(\left( \frac{19}{40} \right) \times 100\)
- Calculation:
\[ P3 = \left( \frac{19}{40} \right) \times 100 = \frac{1900}{40} = 47.5\% \]

4. **Transaction IV:**
- Cost Price (C.P) = Rs 60
- Profit = Rs 29
- Percentage Profit (P4) = \(\left( \frac{29}{60} \right) \times 100\)
- Calculation:
\[ P4 = \left( \frac{29}{60} \right) \times 100 = \frac{2900}{60} \approx 48.33\% \]

### Summary of Percentage Profits:
- Transaction I: 47.22%
- Transaction II: 48%
- Transaction III: 47.5%
- Transaction IV: 48.33%

### Conclusion:
The best transaction in terms of percentage profit is **Transaction IV** with a profit percentage of **48.33%**.

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