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in Commercial Mathematics by (31.2k points)
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A can do a piece of work in 24 hours while B alone can do it in 16 hours. If A, B and C working together can finish it in 8 hours, in how many hours can C alone finish the work?

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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.

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