A wall of 100 metres can be built by 7 men or 10 women in 10 days. How many days will 14 men and 20 women take to build a wall of 600 metres ?

Options

A. 15
B. 20
C. 25
D. 30

Answer

To solve the problem step by step, we will first determine the work done by men and women in terms of a common unit, then calculate how long it will take for 14 men and 20 women to build a wall of 600 meters.

### Step 1: Determine the work done by men and women
Given that:
- 7 men can build a wall of 100 meters in 10 days.
- 10 women can also build a wall of 100 meters in 10 days.

From this, we can find the work done by one man and one woman.

### Step 2: Calculate the work done by one man in one day
The total work done (in terms of wall area) can be calculated as:
- Work done by 7 men in 10 days = 100 meters
- Therefore, work done by 1 man in 10 days = 100 meters / 7 = approximately 14.29 meters.

Now, work done by 1 man in 1 day:
\[ \text{Work done by 1 man in 1 day} = \frac{14.29 \text{ meters}}{10 \text{ days}} = 1.429 \text{ meters/day} \]

### Step 3: Calculate the work done by one woman in one day
Similarly, for women:
- Work done by 10 women in 10 days = 100 meters
- Therefore, work done by 1 woman in 10 days = 100 meters / 10 = 10 meters.

Now, work done by 1 woman in 1 day:
\[ \text{Work done by 1 woman in 1 day} = \frac{10 \text{ meters}}{10 \text{ days}} = 1 \text{ meter/day} \]

### Step 4: Convert the workforce of 14 men and 20 women into equivalent work done per day
Now, we can calculate the total work done by 14 men and 20 women in one day:
- Work done by 14 men in one day:
\[ \text{Work done by 14 men} = 14 \times 1.429 \text{ meters/day} = 20.006 \text{ meters/day} \]
- Work done by 20 women in one day:
\[ \text{Work done by 20 women} = 20 \times 1 \text{ meter/day} = 20 \text{ meters/day} \]

### Step 5: Total work done by 14 men and 20 women in one day
Now, adding both contributions:
\[ \text{Total work done in one day} = 20.006 + 20 = 40.006 \text{ meters/day} \]

### Step 6: Calculate the time required to build 600 meters
To find out how many days it will take to build a wall of 600 meters:
\[ \text{Days required} = \frac{600 \text{ meters}}{40.006 \text{ meters/day}} \approx 14.99 \text{ days} \]

Since we cannot have a fraction of a day in practical terms, we round it up to 15 days.

### Final Answer:
It will take approximately **15 days** for 14 men and 20 women to build a wall of 600 meters.

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