Question

A and B complete a piece of work in $24$ days. B and C do the same work in $36$ days; and A and B and C together finish it in $18$ days. In how many days will C alone complete the work ?

• A. $45$ days
• B. $18$ days
• C. $20$ days
• D. $72$ days

Answer 1

The correct option is D $72$ days

(A+B+C)' s 1 Day work $=\frac{1}{18}$
(A+B)'s 1 Day work $=\frac{1}{24}$
C's 1 day work $=\frac{1}{18}-\frac{1}{24}$
$=\frac{4-3}{72}=\frac{1}{72}$
Hence C alone complete work in $72$ days