Question

3 men, 5 women, and 7 children can complete a work in 40 days. 6 men, 10 women, and 18 children can complete the work in 18 days. 9 men, 15 women, and 5 children can complete the work in?

• A. 17 17/18 days
• B. 18 18/19 days
• C. 19 18/19 days
• D. 18 17/18 days
• E. 18 days

Hint:

Work problems can be solved using the formula \( \text{Work} = \text{Workforce} \times \text{Time} \), and solving for time gives the solution.

Answer 1

The Correct Option is B

Step 1: Identifying the formula.
The work done is given by: \[ \text{Work} = \text{Workforce} \times \text{Time} = 720C \] Let the efficiency of men be \( A \), women be \( W \), and children be \( C \). The total workforce is: \[ 3A + 5W + 7C = 720C \] Step 2: Solving the equations.
From the first equation \( 3A + 5W + 7C = 720C \), we have: \[ \text{Workforce for 6 men, 10 women, and 18 children:} \] \[ 6A + 10W + 18C = 720C \] This simplifies to: \[ 40A + 280C = 36A + 324C \] Simplifying further gives \( A = 11C \). Substituting this into the first equation results in \( n = 720 \). Now, calculate for 9 men, 15 women, and 5 children: \[ 9 \times A = 18 18/19 \text{ days} \] Final Answer: \[ \boxed{18 \frac{18}{19} \text{ days}} \]