If 10 men take 6 days to construct a garage, how many more men are needed if the garage is to be constructed in 5 days ?

Answer

To solve the problem step by step, we will use the concept of work done, which is based on the relationship between the number of workers, the number of days they work, and the total work done.

### Step 1: Understand the given information
We know that:
- 10 men can complete the construction of a garage in 6 days.

### Step 2: Set up the relationship
We can use the formula relating the number of men (n), the number of days (d), and the work done (W):
\[ n_1 \times d_1 = n_2 \times d_2 \]
Where:
- \( n_1 = 10 \) (initial number of men)
- \( d_1 = 6 \) (initial number of days)
- \( n_2 \) = ? (number of men needed for 5 days)
- \( d_2 = 5 \) (new number of days)

### Step 3: Substitute the known values into the equation
Substituting the known values into the equation gives:
\[ 10 \times 6 = n_2 \times 5 \]

### Step 4: Calculate the total work done
Calculating the left side:
\[ 60 = n_2 \times 5 \]

### Step 5: Solve for \( n_2 \)
To find \( n_2 \), divide both sides by 5:
\[ n_2 = \frac{60}{5} \]
\[ n_2 = 12 \]

### Step 6: Determine how many more men are needed
Now we know that 12 men are required to complete the garage in 5 days. Since we initially have 10 men, we need to find out how many more men are needed:
\[ \text{More men needed} = n_2 - n_1 \]
\[ \text{More men needed} = 12 - 10 \]
\[ \text{More men needed} = 2 \]

### Final Answer
Thus, **2 more men are needed** to complete the garage in 5 days.

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