A4 days
B8 days
C13 days
D5 days
Answer:
B. 8 days
Read Explanation:
Understanding the Problem: Time and Work
This problem falls under the Time and Work section, a common topic in competitive exams. It requires calculating the combined effort of different individuals (men and women) with varying work efficiencies to complete a task.
Calculating Individual Efficiency
Men's Efficiency: 5 men complete a work in 16 days. This means the total work done by 5 men is equivalent to 1 unit of work in 16 days.
Therefore, the work done by 1 man in 1 day is $\frac{1}{5 \times 16} = \frac{1}{80}$ of the total work.
Women's Efficiency: 2 women complete the same work in 20 days.
Therefore, the work done by 1 woman in 1 day is $\frac{1}{2 \times 20} = \frac{1}{40}$ of the total work.
Calculating Combined Efficiency for the Target Group
We need to find the time taken by 4 women and 2 men to complete the work.
Work done by 2 men in 1 day: $2 \times \frac{1}{80} = \frac{1}{40}$ of the total work.
Work done by 4 women in 1 day: $4 \times \frac{1}{40} = \frac{1}{10}$ of the total work.
Total work done by 4 women and 2 men in 1 day: $\frac{1}{40} + \frac{1}{10} = \frac{1 + 4}{40} = \frac{5}{40} = \frac{1}{8}$ of the total work.
Calculating the Total Time
If $\frac{1}{8}$ of the work is completed in 1 day by 4 women and 2 men, then the total time required to complete the entire work is the reciprocal of this fraction.
Time taken = $\frac{1}{\frac{1}{8}}$ = 8 days.