25 men can reap a field in 20 days. When should 15men leave the work, if the whole field is to be reaped in 35 days after they leave the work?

Options

A. After 5 days
B. After 10 days
C. After 9 days
D. After 7 days

Answer

To solve the problem step by step, we will use the concept of work done and the unitary method.

### Step 1: Calculate the total work in man-days.
Given that 25 men can reap a field in 20 days, we can calculate the total work in man-days as follows:

Total work = Number of men × Number of days
Total work = 25 men × 20 days = 500 man-days

### Step 2: Determine the work done by 15 men.
Next, we need to find out how much work 15 men can do in a certain number of days. Let’s denote the number of days that 15 men work before they leave as \( x \).

Work done by 15 men in \( x \) days = 15 men × \( x \) days = 15x man-days

### Step 3: Calculate the remaining work after 15 men leave.
After 15 men leave, the remaining work will be:

Remaining work = Total work - Work done by 15 men
Remaining work = 500 man-days - 15x man-days

### Step 4: Determine the work done by the remaining men.
After 15 men leave, there will be 10 men left (since 25 - 15 = 10 men). We know that the remaining work must be completed in 35 days.

Work done by 10 men in 35 days = 10 men × 35 days = 350 man-days

### Step 5: Set up the equation.
Now we can set up the equation for the remaining work:

Remaining work = Work done by 10 men in 35 days
500 - 15x = 350

### Step 6: Solve for \( x \).
Now we will solve the equation for \( x \):

500 - 15x = 350
=> 15x = 500 - 350
=> 15x = 150
=> x = 150 / 15
=> x = 10

### Conclusion:
15 men should leave the work after 10 days.