Mohan can complete a piece of work alone in 6 days by working 5 hours a day, and Rohan can do the same in 8 days. If they work together for 8 hours each day, how long will it take them to finish the work?
\(2\frac{1}{7}\) days
Mohan finishes the work in \(6\) days at \(5\) hours a day, so the whole work needs \(6 \times 5 = 30\) Mohan-hours, giving Mohan a rate of \(\dfrac{1}{30}\) of the work per hour.
Rohan finishes the same work in \(8\) days at \(5\) hours a day, i.e. \(8 \times 5 = 40\) Rohan-hours, giving Rohan a rate of \(\dfrac{1}{40}\) of the work per hour.
Working together, their combined rate per hour \(= \dfrac{1}{30} + \dfrac{1}{40} = \dfrac{4 + 3}{120} = \dfrac{7}{120}\) of the work.
In one day of \(8\) hours they complete \(8 \times \dfrac{7}{120} = \dfrac{56}{120} = \dfrac{7}{15}\) of the work.
Time to finish the whole work \(= \dfrac{1}{\,7/15\,} = \dfrac{15}{7} = 2\dfrac{1}{7}\) days.
Hence, they will finish the work in \(2\frac{1}{7}\) days.
Important Questions from Time and Work
Mohan can do a piece of work in 10 days and Sohan in 15 days. They started working together, but after 3 days Mohan left the work . What time will Sohan take to finish the work?
A tank is filled in 8 hours by three taps A, B and C. The tap C is thrice as fast as B and B is twice as fast as A. How much time will pipe B alone take to fill the tank?
Had been one menless, then the number of days required to do a piece of work would have been one more. If the number of Man. Days required to complete the work is 56, how many workers were there?
A can do a piece of work in 16 hours, B and C can do it in 8 hours while A and C can do it 12 hours. How long will B alone take to do it?
- lf 12 men can do a work in 20 days, in how many days will the work be done by 15 men-
