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Fill in the blanks. (i) A tap can fill a tank in 6 hours. The part of the tank filled in 1 hour is…………… (ii) A and B working together can finish a piece of work in 6 hours while A alone can do it in 9 hours. B alone can do it in ……….. hours. (iii) A can do a work in 16 hours and B alone can do it in 24 hours. If A, B and C working together can finish it in 8 hours, then C alone can finish it in ……….. hours.(iv) If A's one day's work is 3/20, then A can finish the whole work in……… days. |
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Answer» (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 ∴ \(\frac{20}{3}=6\frac{2}{3}\) |
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