6 Men+10 women can reep 5/12 part of 360 hectare land in 15 days by working 6 Hrs per day. If now 2 more men and 4 women are employed. then the work will be finished in how many days by working 7 Hrs per day. it is also given that work ratio of 2 man = 3 women?

Options

A. a)13.25
B. b)13.25
C. c)14.25
D. d)14.15

Answer

To solve the problem step by step, we will follow the given information and perform the necessary calculations.

### Step 1: Calculate the total work done
Given that 6 men and 10 women can reap \( \frac{5}{12} \) of 360 hectares in 15 days by working 6 hours per day.

First, we calculate the total area of land:
\[ \text{Total area} = 360 \text{ hectares} \]

Now, calculate the area reaped:
\[ \text{Area reaped} = \frac{5}{12} \times 360 = 150 \text{ hectares} \]

Next, we calculate the total work done in terms of man-hours:
\[ \text{Total man-hours} = \text{Number of days} \times \text{Hours per day} = 15 \times 6 = 90 \text{ hours} \]

### Step 2: Calculate the efficiency of 6 men and 10 women
Let’s denote the work done by 1 man in 1 hour as \( M \) and the work done by 1 woman in 1 hour as \( W \).

From the problem, we know that:
\[ 6M + 10W \text{ can complete } 150 \text{ hectares in } 90 \text{ hours.} \]

Thus, the total work done in man-hours is:
\[ (6M + 10W) \times 90 = 150 \]
\[ 6M + 10W = \frac{150}{90} = \frac{5}{3} \]

### Step 3: Convert men to women using the given ratio
We are given the ratio \( 2M = 3W \), which implies:
\[ M = 1.5W \]

Substituting \( M \) in the equation:
\[ 6(1.5W) + 10W = \frac{5}{3} \]
\[ 9W + 10W = \frac{5}{3} \]
\[ 19W = \frac{5}{3} \]
\[ W = \frac{5}{57} \]

Now substituting back to find \( M \):
\[ M = 1.5W = 1.5 \times \frac{5}{57} = \frac{7.5}{57} = \frac{5}{38} \]

### Step 4: Calculate the remaining work
The total work in terms of units is:
\[ \text{Total work} = 360 \text{ hectares} = 360 \text{ units} \]

The work already done is:
\[ \text{Work done} = 150 \text{ hectares} = 150 \text{ units} \]

Remaining work:
\[ \text{Remaining work} = 360 - 150 = 210 \text{ units} \]

### Step 5: Calculate the new workforce
Now, 2 more men and 4 more women are employed:
\[ \text{New number of men} = 6 + 2 = 8 \]
\[ \text{New number of women} = 10 + 4 = 14 \]

Convert men to women:
\[ 8M = 8 \times 1.5W = 12W \]

Total workforce in terms of women:
\[ \text{Total women} = 12W + 14W = 26W \]

### Step 6: Calculate the time to finish the remaining work
Now, they will work for 7 hours a day. The total work done in one day is:
\[ \text{Daily work} = 26W \times 7 \text{ hours} = 182 \text{ units} \]

To find the number of days required to finish the remaining work:
\[ \text{Days required} = \frac{\text{Remaining work}}{\text{Daily work}} = \frac{210}{182} \approx 1.15 \text{ days} \]

### Final Answer
Thus, the work will be finished in approximately **1.15 days**.