15 men take 42 days of 4 hours each to do a piece of work. How many days of 6 hours each would 21 women take if 3 women do as much work as 2 men?

Options

A. 15
B. 22
C. 25
D. 30

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Calculate the total work done in man-hours
Given that 15 men take 42 days of 4 hours each to complete a piece of work, we first calculate the total work in terms of man-hours.

\[ \text{Total work} = \text{Number of men} \times \text{Number of days} \times \text{Hours per day} \]
\[ \text{Total work} = 15 \text{ men} \times 42 \text{ days} \times 4 \text{ hours/day} \]
\[ \text{Total work} = 15 \times 42 \times 4 = 2520 \text{ man-hours} \]

### Step 2: Determine the work done by one woman
We know from the problem that 3 women do as much work as 2 men. Therefore, we can find the equivalent work done by one woman in terms of man-hours.

Let the work done by one man in one hour be 1 unit of work. Then:
- Work done by 2 men in one hour = 2 units
- Work done by 3 women in one hour = 2 units

Thus, the work done by one woman in one hour is:
\[ \text{Work done by 1 woman in 1 hour} = \frac{2 \text{ units}}{3} = \frac{2}{3} \text{ units} \]

### Step 3: Calculate the work done by 21 women in one hour
Now, we calculate how much work 21 women can do in one hour:
\[ \text{Work done by 21 women in 1 hour} = 21 \times \frac{2}{3} = 14 \text{ units} \]

### Step 4: Calculate the total time taken by 21 women to complete the work
Now, we need to find out how many hours it would take for 21 women to complete the total work of 2520 man-hours.

Using the formula:
\[ \text{Total time (in hours)} = \frac{\text{Total work}}{\text{Work done by 21 women in 1 hour}} \]
\[ \text{Total time (in hours)} = \frac{2520}{14} = 180 \text{ hours} \]

### Step 5: Convert hours into days of 6 hours each
Finally, we need to convert the total hours into days, where each day consists of 6 working hours:
\[ \text{Total days} = \frac{\text{Total time (in hours)}}{\text{Hours per day}} \]
\[ \text{Total days} = \frac{180}{6} = 30 \text{ days} \]

### Final Answer
Therefore, 21 women would take **30 days of 6 hours each** to complete the work.

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