If 25 men can reap a crop in 60 days, then in how many days will 10 men reap the crop ?

Question

Accepted Answer

To determine how many days 10 men will take to reap the crop, we can use the concept of man-days, which is the product of the number of men and the number of days they work. This concept helps us understand the total amount of work required to complete a task.

1. **Calculate the total man-days required to reap the crop:**

- Given that 25 men can reap the crop in 60 days, the total man-days required is:
     $$
     25 \text{ men} \times 60 \text{ days} = 1500 \text{ man-days}
     $$

2. **Determine how many days 10 men will take:**

- If 10 men are working, we need to find out how many days they will take to complete the same amount of work (1500 man-days).
   - Let $ x $ be the number of days 10 men will take. Therefore, the equation is:
     $$
     10 \text{ men} \times x \text{ days} = 1500 \text{ man-days}
     $$
   - Solving for $ x $:
     $$
     x = \frac{1500 \text{ man-days}}{10 \text{ men}} = 150 \text{ days}
     $$

Thus, 10 men will take 150 days to reap the crop, which corresponds to Option 4.

**Explanation of why other options are incorrect:**

- **Option 1 (125 days):** If 10 men were to complete the work in 125 days, the total man-days would be:
  $$
  10 \text{ men} \times 125 \text{ days} = 1250 \text{ man-days}
  $$
  This is less than the required 1500 man-days, so 125 days is insufficient.

- **Option 2 (92 days):** If 10 men were to complete the work in 92 days, the total man-days would be:
  $$
  10 \text{ men} \times 92 \text{ days} = 920 \text{ man-days}
  $$
  This is significantly less than the required 1500 man-days, making 92 days incorrect.

- **Option 3 (100 days):** If 10 men were to complete the work in 100 days, the total man-days would be:
  $$
  10 \text{ men} \times 100 \text{ days} = 1000 \text{ man-days}
  $$
  This is also less than the required 1500 man-days, so 100 days is not enough.

Therefore, the correct answer is Option 4, which is 150 days.