Number of hours A required do a piece of work : 24 hours
Number of hours B required do a piece of work : 16 hours
Let number of hours C required to do a piece of work : X hours
Number of hours required by A, B and C together to do a piece of work : 8 hours
Work done by A in one hour: \(\frac{1}{24}\)
Work done by B in one hour: \(\frac{1}{16}\)
Work done by C in one hour: \(\frac{1}{x}\)
Work done by A, B and C together in a one hour : \(\frac{1}{8}\)
Work done by A, B and C together in one hour :
\(\therefore \frac{5x\,+\,48}{48x}=\frac{1}{8}\)
⇒ 40X +384 = 48X
⇒ 8X = 384
⇒ X = \(\frac{384}{8}\) = 48 hours
∴ Siraj can do the work 48 hours.