If 20 men can build a wall 112 metres long in 6 days, what length of a similar wall can be built by 25 men in 3 days ?

Options

A. 140 metres
B. 44.8 metres
C. 105 metres
D. 70 metres

Answer

To solve the problem, we need to determine how much work can be done by 25 men in 3 days, given that 20 men can build a wall 112 meters long in 6 days. We can use the concept of work, which is defined as the product of the number of men, the number of days, and the hours worked per day. However, since we are not given the hours, we can simplify our calculations.

### Step-by-Step Solution:

1. **Calculate the total work done by the first group of men**:
- The work done (W1) by 20 men in 6 days can be calculated as:
\[ W_1 = \text{Number of men} \times \text{Number of days} = 20 \times 6 = 120 \text{ man-days} \]
- Since they build a wall of 112 meters, we can say:
\[ 120 \text{ man-days} \rightarrow 112 \text{ meters} \]

2. **Calculate the work done per meter**:
- The work done per meter is:
\[ \text{Work per meter} = \frac{120 \text{ man-days}}{112 \text{ meters}} = \frac{120}{112} = \frac{15}{14} \text{ man-days per meter} \]

3. **Calculate the total work that can be done by the second group of men**:
- For 25 men working for 3 days, the total work (W2) they can do is:
\[ W_2 = \text{Number of men} \times \text{Number of days} = 25 \times 3 = 75 \text{ man-days} \]

4. **Calculate the length of the wall that can be built by the second group**:
- To find the length of the wall (L) that can be built by 75 man-days, we use the work per meter calculated earlier:
\[ L = \frac{\text{Total work}}{\text{Work per meter}} = \frac{75 \text{ man-days}}{\frac{15}{14} \text{ man-days per meter}} = 75 \times \frac{14}{15} \]
- Simplifying this gives:
\[ L = \frac{75 \times 14}{15} = 5 \times 14 = 70 \text{ meters} \]

### Final Answer:
The length of the wall that can be built by 25 men in 3 days is **70 meters**.