Question

'A','B', and 'C' working together can fo a piece of work in 8 hours. 'A' alone can do it in 20 hours and 'B' can do it in 24 hours. In his many hours will 'C' alone do the same work?

Answer 1

Let the hours taken by C to complete the work be x.
Now,
(A+B+C)'s one day work=1/8
One day work of A=1/20
One day work of B=1/24
A/q
$\frac{1}{20} + \frac{1}{24} + x = \frac{1}{8} \\ x = \frac{1}{8} - \frac{1}{20} - \frac{1}{24} \\ x = \frac{15 - 6 - 5}{120}$
$x = \frac{4}{ 120} = \frac{1}{30}$
Hence,C can alone do the work in 30 hrs