Question

A can do half of a work in 5 days. B can do three-fifth of the same work in 9 days and C can do two-third of that work in 8 days. In how many days can three of them together complete the work?

• A. 5 days
• B. $4\frac{1}{2}$ days
• C. 3 days
• D. 4 days

Answer 1

The correct option is D 4 days

Given, A can do half of a work in 5 days.
Hence, A can do the entire work in 10 days.

Given, B can do three-fifth of the same work in 9 days.
Hence,B can do the entire work in $\frac{9\times 5}{3}$ days = 15 days

Given, C can do two-third of that work in 8 days.
Hence, C can do the entire work in $\frac{8\times 3}{2}$ days = 12 days

$\therefore (A+B+C{)}^{\prime }s$ amount of work done in one day
$=\frac{1}{10}+\frac{1}{15}+\frac{1}{12}=\frac{6+4+5}{60}=\frac{15}{60}=\frac{1}{4}$

So, A, B and C together can do $\frac{1}{4}$ part of work in 1 day.
$\therefore$ They will complete the work in 4 days.