Question

12 men and 6 women can complete a work in 10 days. 3 men and 6 women can complete this work in 25 days. How many men are required to complete this work in 5 days?

• A. 30
• B. 20
• C. 24
• D. 36

Answer 1

The Correct Option is A

Number of Men Required Calculation

Step 1: Understanding the Variables 

Let the amount of work done by:

• 1 man in 1 day = M
• 1 woman in 1 day = W

Step 2: Calculate the Total Work

From the first condition:

\[ 12M \times 10 + 6W \times 10 = \text{Total work} \] \[ 120M + 60W = \text{Total work} \]

From the second condition:

\[ 3M \times 25 + 6W \times 25 = \text{Total work} \] \[ 75M + 150W = \text{Total work} \]

Step 3: Solving the System of Equations

Subtracting the two equations:

\[ (120M + 60W) - (75M + 150W) = 0 \] \[ 45M - 90W = 0 \implies M = 2W \]

Step 4: Finding the Total Work

Substituting \( M = 2W \) into the first equation:

\[ 120(2W) + 60W = \text{Total work} \] \[ 240W + 60W = 300W \]

Step 5: Finding the Number of Men Required

Let the number of men required be x. The work done by x men in 5 days is:

\[ 5 \times x \times M = 300W \] Substituting \( M = 2W \): \[ 5 \times x \times 2W = 300W \] \[ 10xW = 300W \] \[ x = 30 \]

Step 6: Conclusion

The number of men required to complete the work in 5 days is 30.