Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the
same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and
works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had
started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had
worked on every third day, then the number of days required to complete the task would have been
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Explanatory Answer
1/A + 1/V= 1/ 150 ------------(1)
1/V + 1/S= 1/ 100 ------------(2)
75/A + 135/V+ 45/S= 1 ----(3)
Subtracting eqn (1) from eqn(2),
1/S – 1/A= 1/300 -----(4)
Multiplying eqn (1) with 135, we get 135/A + 135/V= 135/150= 9/10 --------(5)
Subracting eqn (5) from eqn (3), -60/A + 45/S= 1/10-----(6)
Solving, eqn (4) and eqn (6), we get 1/S= 1/150, 1/A= 1/300 . Substituting the value of 1/S in eqn (2) we get 1/V = 1/300.
Anil takes 300 days to finish the task.
Vimal takes 300 days to finish the task.
Sunil takes 150 days to finish the task.
Let total work= 300 units
Anil does 1 unit/day.
Vimal does 1 unit/day.
Sunil does 2 units/day.
If Anil works for 6k days, Vimal works for 3k days and Sunil works for 2k days.
If 6k= 138 days.
Anil would have finished 138 units, Vimal would have completed 69 units and Sunil would have finished 46*2= 92 units.
138+69+92= 299 units would be completed.
In 139th day, only Anil works and therefore (299+1= 300 units) work is finished.
Total work got completed in 139 days.
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