(i) \(\frac{1}{6}\)
If A can do a piece of work in n days, then A can do \(\frac{1}{n}\) of the work in on day
(ii) 18
Number of hours A required do a piece of work : 9 hours
Let number of hours B required do a piece of work : X hours
Number of hours required by A and B together to do a piece of work : 6 hours
Work done by A in one hour: \(\frac{1}{9}\)
Work done by B in one hour: \(\frac{1}{x}\)
Work done by A and B together in a hour: \(\frac{1}{6}\)
Work done by A and B together in one hour: \(\frac{1}{9}+\frac{1}{x}=\frac{x\,+\,9}{9x}=\frac{1}{6}\)
∴ \(\frac{x\,+\,9}{9x}=\frac{1}{6}\)
⇒ 6X +54 = 9X
⇒ 3X = 54
⇒ X = \(\frac{54}{3}=18\)
∴ B can do the work 18 hours
(iii) 48
Number of hours A required do a piece of work : 16 hours
Number of hours B required do a piece of work : 24 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: \(\frac{1}{16}\)
Work done by B in one hour: \(\frac{1}{24}\)
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 : \(\frac{1}{16}+\frac{1}{24}+\frac{1}{x}=\frac{5}{48}+\frac{1}{x}\)
= \(\frac{5x\,+\,48}{48x}=\frac{1}{8}\)
∴ \(\frac{5x\,+\,48}{48x}=\frac{1}{8}\)
⇒ 40X +384 = 48X
⇒ 8X = 384
⇒ X = \(\frac{384}{8}\) = 48 hours
∴ C can do the work 48 hours.
(iv) \(6\frac{2}{3}\)
If A can do a piece of work in n days, then A can do \(\frac{1}{n}\) of the work in on day
∴ \(\frac{20}{3}=6\frac{2}{3}\)
