Twenty men can lay a road off 50 km long in 10 days. In how many days can 15 men lay a road of 75 km long?

Options

A. 10 days
B. 20 days
C. 30 days
D. 40 days

Explanation

To solve the problem, we can use the concept of work done, which relates the number of men, the days taken, and the work done (in kilometers of road laid).

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Number of men (m1) = 20
- Days (d1) = 10
- Work done (w1) = 50 km
- Number of men (m2) = 15
- Work to be done (w2) = 75 km
- Days (d2) = ?

2. **Set Up the Proportion:**
We know that the work done is directly proportional to the number of men and the number of days. We can set up the equation as follows:
\[ \frac{m1 \cdot d1}{w1} = \frac{m2 \cdot d2}{w2} \]

3. **Substitute the Known Values:**
Plugging in the values we have:
\[ \frac{20 \cdot 10}{50} = \frac{15 \cdot d2}{75} \]

4. **Simplify the Left Side:**
Calculate the left side:
\[ \frac{200}{50} = 4 \]
So, we have:
\[ 4 = \frac{15 \cdot d2}{75} \]

5. **Cross-Multiply to Solve for d2:**
Cross-multiplying gives us:
\[ 4 \cdot 75 = 15 \cdot d2 \]
This simplifies to:
\[ 300 = 15 \cdot d2 \]

6. **Isolate d2:**
To find d2, divide both sides by 15:
\[ d2 = \frac{300}{15} = 20 \]

### Final Answer:
Thus, 15 men can lay a road of 75 km long in **20 days**.

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