If 5 men or 9 women can do a piece of work in 19 days. 3 men and 6 women will do the same work in how many days ?

Options

A. 10 days
B. 12 days
C. 13 days
D. 15 days

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the Work Capacity
We know that:
- 5 men can complete the work in 19 days.
- 9 women can also complete the same work in 19 days.

This implies that the work done by 5 men is equal to the work done by 9 women in the same time frame.

### Step 2: Determine the Work Done in Terms of Women
Since 5 men can do the work in 19 days, we can express the total work in terms of women.

Let’s find out how much work 1 man does in terms of women:
- The work done by 5 men in 19 days = Work done by 9 women in 19 days.

Thus, we can set the efficiency of 1 man (m) in terms of women (w):
- 5m = 9w
- Therefore, 1m = 9/5w

### Step 3: Convert Men to Women in the Given Scenario
Now, we need to find out how many days it will take for 3 men and 6 women to complete the work.

First, convert the 3 men into women:
- 3 men = 3 * (9/5) women = 27/5 women.

Now, add the 6 women:
- Total women = 27/5 + 6 = 27/5 + 30/5 = 57/5 women.

### Step 4: Calculate the Total Work
Now we know that 9 women can complete the work in 19 days. Therefore, the total work can be expressed as:
- Total work = Number of women * Number of days = 9 women * 19 days = 171 women-days.

### Step 5: Set Up the Equation for 3 Men and 6 Women
Let x be the number of days it takes for 57/5 women to complete the same work. We can set up the equation:
- (57/5) women * x days = 171 women-days.

### Step 6: Solve for x
Now we can solve for x:
- x = Total work / Efficiency = 171 / (57/5)
- x = 171 * (5/57)
- x = 15 days.

### Conclusion
Thus, 3 men and 6 women will complete the work in **15 days**.

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