In terms of percentage profit, which is the best transaction? | | C.P. (in ₹) | Profit (in ₹) | |---|---|---| | (a) | 36 | 17 | | (b) | 50 | 24 | | (c) | 40 | 19 | | (d) | 60 | 29 |

### Concept & Comparing Profit Percentages To determine the "best" transaction, we must find the one with the highest profit percentage. Profit percentage is the ratio of profit to cost price, expressed as a percentage. $$ \text{Profit \%} = \left( \frac{\text{Profit}}{\text{C.P.}} \right) \times 100 $$ ### Step-by-Step Solution Given four transactions, we need to calculate the approximate profit percentage for each to compare them. Calculation: 1. **Transaction (a):** Profit = 17, C.P. = 36. $$ \text{Profit \%} = \left(\frac{17}{36}\right) \times 100 \approx 47.22\% $$ 2. **Transaction (b):** Profit = 24, C.P. = 50. $$ \text{Profit \%} = \left(\frac{24}{50}\right) \times 100 = 48.00\% $$ 3. **Transaction (c):** Profit = 19, C.P. = 40. $$ \text{Profit \%} = \left(\frac{19}{40}\right) \times 100 = 47.50\% $$ 4. **Transaction (d):** Profit = 29, C.P. = 60. $$ \text{Profit \%} = \left(\frac{29}{60}\right) \times 100 \approx 48.33\% $$ Comparing the percentages: $48.33\% > 48.00\% > 47.50\% > 47.22\%$. Transaction (d) yields the highest profit margin. ### Exam Strategy & Shortcut Instead of computing full percentages, estimate the fractions relative to $1/2$ (or 50%). (a) 17 is 1 less than 18 (which is half of 36). (b) 24 is 1 less than 25 (half of 50). (c) 19 is 1 less than 20 (half of 40). (d) 29 is 1 less than 30 (half of 60). Since they are all "1 less than half", the fraction with the largest denominator will be the closest to $1/2$ (50%). Thus, $29/60$ is the largest value. ### Common Pitfall Misinterpreting "best transaction" as simply the highest absolute profit (which also happens to be 29 here, but wouldn't always be the case if the CP was much higher). Always compare percentages. ### Final Answer Therefore, the correct answer is **(d)**.