Fifteen men can build a wall in 60 days. How many more men are required to build another wall of same size in 45 days ?

Answer

To solve the problem step by step, we can use the concept of inverse variation. Here's how we can approach it:

### Step 1: Understand the relationship between men, days, and work
We know that 15 men can build a wall in 60 days. This means that the amount of work done is constant.

### Step 2: Set up the equation
Let \( x \) be the number of men required to build the wall in 45 days. According to the inverse variation principle, we can set up the relationship as follows:

\[ \text{Men} \times \text{Days} = \text{Constant Work} \]

For the first scenario:
\[ 15 \text{ men} \times 60 \text{ days} = \text{Constant Work} \]

For the second scenario:
\[ x \text{ men} \times 45 \text{ days} = \text{Constant Work} \]

### Step 3: Set the equations equal
Since both expressions equal the same constant work, we can write:

\[ 15 \times 60 = x \times 45 \]

### Step 4: Solve for \( x \)
Now we can solve for \( x \):

\[ 900 = x \times 45 \]

To isolate \( x \), divide both sides by 45:

\[ x = \frac{900}{45} \]

Calculating this gives:

\[ x = 20 \]

### Step 5: Determine how many more men are needed
We found that 20 men are required to build the wall in 45 days. However, we need to find out how many more men are required compared to the original 15 men.

\[ \text{More men required} = x - 15 = 20 - 15 = 5 \]

### Final Answer
Thus, **5 more men** are required to build another wall of the same size in 45 days.

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