18 men or 36 boys working 6 hours a day can plough a field in 24 days. In how many days will 24 men and 24 boys working 9 hours a day plough the same field?

Options

A. 9
B. 10
C. 6
D. 8

Answer

To solve the problem, we will first determine the total work done in terms of man-hours and then calculate how many days it will take for 24 men and 24 boys working 9 hours a day to complete the same work.

### Step 1: Calculate the total work done in man-hours

Given:
- 18 men or 36 boys can plough the field in 24 days working 6 hours a day.

First, we need to find the total work done in man-hours.

**Total work (in man-hours) = Number of workers × Hours per day × Number of days**

Using men:
- Number of men = 18
- Hours per day = 6
- Days = 24

Total work = 18 men × 6 hours/day × 24 days = 2592 man-hours

### Step 2: Convert boys to men

We know that 36 boys are equivalent to 18 men. Therefore, we can also express the work done in terms of boys if needed, but since we are focusing on men, we will continue with the man-hours.

### Step 3: Calculate the work done by 24 men and 24 boys

Next, we need to find out how much work 24 men and 24 boys can do in one day.

**Convert boys to men:**
- Since 36 boys = 18 men, then 24 boys = 12 men.

So, the total number of men equivalent from 24 men and 24 boys:
- Total equivalent men = 24 men + 12 men = 36 men.

### Step 4: Calculate the daily work done by 36 men

Now, we calculate how much work 36 men can do in one day working 9 hours a day.

**Daily work = Number of workers × Hours per day**
- Daily work = 36 men × 9 hours/day = 324 man-hours/day.

### Step 5: Calculate the number of days required to complete the work

Now, we need to find out how many days it will take for 36 men working 9 hours a day to complete the total work of 2592 man-hours.

**Number of days = Total work / Daily work**
- Number of days = 2592 man-hours / 324 man-hours/day = 8 days.

### Final Answer:
It will take 24 men and 24 boys working 9 hours a day a total of **8 days** to plough the same field.

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