Question

It 10 men or 20 women or 40 children can do a piece of work in 7 months, then 5 men, 5 women and 5 children together can do half of the work in :

• A. 6 months
• B. 4 months
• C. 5 months
• D. 8 months

Answer 1

Answer: (B)

4 months

Let total work be $W$

Work done by $1$ man in $1$ month = $\frac{W}{10\ast 7}=\frac{W}{70}$

Work done by $1$ woman in $1$ month = $\frac{W}{20\ast 7}=\frac{W}{140}$

Work done by $1$ child in $1$ month = $\frac{W}{40\ast 7}=\frac{W}{280}$

Total work done by 5 men, 5 women and 5 children in 1 month= $\frac{5W}{70}+\frac{5W}{140}+\frac{5W}{280}=\frac{W}{8}$

Let number of months be $n$

$\frac{W}{8}\ast n=\frac{W}{2}$

n=4