If 5 men can build a wall in 12 days, how many men can build it in 10 days?

Answer

To solve the problem step by step, we will use the concept of inverse proportion as explained in the video transcript.

### Step 1: Understand the relationship
We know that if more men are working, they will take fewer days to complete the same work. Therefore, the number of men (n) and the number of days (d) are inversely proportional.

### Step 2: Set up the equation
From the problem, we have:
- 5 men can build the wall in 12 days.
- We need to find out how many men (let's call this x) can build the same wall in 10 days.

Using the concept of inverse proportion, we can set up the equation:
\[ n_1 \times d_1 = n_2 \times d_2 \]
Where:
- \( n_1 = 5 \) (number of men)
- \( d_1 = 12 \) (number of days)
- \( n_2 = x \) (unknown number of men)
- \( d_2 = 10 \) (number of days)

So, we have:
\[ 5 \times 12 = x \times 10 \]

### Step 3: Solve for x
Now, we can solve for x:
\[ 60 = x \times 10 \]
To isolate x, divide both sides by 10:
\[ x = \frac{60}{10} \]
\[ x = 6 \]

### Step 4: Conclusion
Thus, 6 men can build the wall in 10 days.

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