Question

Two motor mechanics, Raju and Siraj, working together can overhaul a scooter in 6 hours. Raju alone can do the job in 15 hours. In how many hours can Siraj alone do it?

Answer 1

Number of hours Raju required to overhaul a scooter : 15 hours 

Let number of hours siraj required to overhaul a scooter : X hours 

Number of hours required by Raju and Siraj together to do a piece of work : 6 hours

Work done by Raju in one hour : \(\frac{1}{15}\)

Work done by Siraj in one hour : \(\frac{1}{x}\)

Work done by Raju and Siraj together in a one hour : \(\frac{1}{6}\)

Work done by Raju and Siraj together in one hour : \(\frac{1}{15}+\frac{1}{x}=\frac{x\,+\,15}{15x}=\frac{1}{6}\)

\(\therefore \frac{x\,+\,15}{15x}=\frac{1}{6}\)

⇒ 6X +90 = 15X 

⇒ 9X = 90

⇒ X = \(\frac{90}{9}\) = 10 hours

∴ Siraj can do the work 10 hours.