A contractor undertakes to complete a work in 20 days. He employs 30 labourers on this job. How many more labourers would he employ to complete the work in 15 days?

Options

A. 50
B. 40
C. 30
D. 10

Answer

To solve the problem step by step, we can follow these steps:

### Step 1: Determine the total work done in terms of laborers and days.
Let the total work be represented as \( W \). If 30 laborers can complete the work in 20 days, we can express the total work as:
\[ W = \text{Number of laborers} \times \text{Number of days} = 30 \times 20 = 600 \text{ labor-days} \]

### Step 2: Calculate the work done by one laborer in one day.
If one laborer does \( x \) amount of work in one day, then the work done by 30 laborers in one day is:
\[ \text{Work done by 30 laborers in one day} = 30x \]
And over 20 days, the total work done is:
\[ \text{Total work} = 20 \times 30x = 600x \]
Since we know the total work \( W = 600 \), we can set this equal to \( 600x \):
\[ 600 = 600x \implies x = 1 \]
This means one laborer does 1 unit of work in one day.

### Step 3: Set up the equation for completing the work in 15 days.
Now, we want to find out how many laborers \( n \) are needed to complete the same work \( W \) in 15 days. If we employ \( n \) additional laborers, the total number of laborers becomes \( 30 + n \). The work done by these laborers in one day is:
\[ \text{Work done by } (30 + n) \text{ laborers in one day} = (30 + n) \times 1 = 30 + n \]
Over 15 days, the total work done will be:
\[ \text{Total work in 15 days} = 15 \times (30 + n) \]

### Step 4: Set the total work equations equal to each other.
We know the total work \( W = 600 \), so we can set up the equation:
\[ 15 \times (30 + n) = 600 \]

### Step 5: Solve for \( n \).
Now, we can simplify and solve for \( n \):
\[ 30 + n = \frac{600}{15} = 40 \]
\[ n = 40 - 30 = 10 \]

### Conclusion:
The contractor would need to employ **10 more laborers** to complete the work in 15 days.

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