20 men can build 56 m wall in 6 days. What length of a similar wall can be build by 70 men in 3 days ?

Options

A. 100m
B. 98m
C. 48m
D. 85m

Answer

To solve the problem step by step, we will use the Unitary Method and the concept of direct proportion.

### Step 1: Understand the given information
We know that:
- 20 men can build a 56 m wall in 6 days.

### Step 2: Determine the work done by one man in one day
To find out how much work one man can do in one day, we first calculate the total work done in terms of man-days.

Total man-days for 20 men in 6 days:
\[ \text{Total man-days} = 20 \text{ men} \times 6 \text{ days} = 120 \text{ man-days} \]

Now, the total work done (length of the wall) is 56 m. Therefore, the work done by one man in one day is:
\[ \text{Work done by one man in one day} = \frac{56 \text{ m}}{120 \text{ man-days}} = \frac{56}{120} = \frac{14}{30} = \frac{7}{15} \text{ m} \]

### Step 3: Calculate the total man-days for 70 men in 3 days
Now, we need to find out how many man-days 70 men will contribute in 3 days:
\[ \text{Total man-days} = 70 \text{ men} \times 3 \text{ days} = 210 \text{ man-days} \]

### Step 4: Calculate the total length of the wall built by 70 men in 3 days
Using the work done by one man in one day, we can find the total length of the wall that can be built by 70 men in 3 days:
\[ \text{Total length of the wall} = \text{Work done by one man in one day} \times \text{Total man-days} \]
\[ = \frac{7}{15} \text{ m} \times 210 \text{ man-days} \]
\[ = \frac{7 \times 210}{15} \]
\[ = \frac{1470}{15} = 98 \text{ m} \]

### Conclusion
Therefore, the length of the wall that can be built by 70 men in 3 days is **98 meters**.

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