Rohit and Virat, working together, can complete an assigned task in 20 days. If Rohit worked alone and completes half the task and then Virat takes over and completes the remaining half, then the task gets completed in 45 days. How long will Rohit take to complete the task if he worked alone? Assume that Rohit is more efficient than Virat.
Let Rohit take 'x' days to complete the task if he worked alone.
Let Virat take 'y' days to complete the task if she worked alone.
Given that They will complete the task in 20 days, if they worked together.
In 1 day, Rohit will complete 1/x of the task.
In 1 day, Virat will complete 1/y of the task.
Together, in 1 day they will complete 120 of the task.
Therefore,1/x + 1/y = 1/20 .... (1)
As per question if Rohit worked alone and completed half the work and then Virat takes over and completes the second half, the task will be completed in 45 days.
Rohit will complete half the task in x/2 days.
Virat will complete half the task in y/2 days.
∴ x/2 + y/2 = 45
Or, x + y = 90 or x = 90 - y .... (2)
Solving 1 and 2 we get
y^2 - 90y + 1800 = 0
=> y 30 or 60
The question clearly states that Rohit is more efficient than Virat. Therefore, Rohit will take lesser time than Virat.
So Rohit will take 30 days