Solution:
Given:
The working efficiency of Raja, Ram and Mohan is 6 : 3 : 2.
Raja can complete the whole work in 10 days.
Raja and Ram together work for the first two days.
Raja and Mohan work for next 4 days.
The remaining work is completed by Mohan.
Formula used:
Work = Efficiency × Time
Calculation:
The working efficiency of Raja = 6k
The working efficiency of Ram = 3k
The working efficiency of Mohan = 2k
Let k = 1,
The working efficiency of Raja = 6 units per day
The working efficiency of Ram = 3 units per day
The working efficiency of Mohan = 2 units per day
The total amount of work or the amount of work done by Raja in 10 days = 6 × 10 = 60 units
Now,
The combined efficiency of Raja and Ram = 6 + 3 = 9 units a day
The total work done by Raja and Ram in first 2 days = 9 × 2 = 18 units
Now,
The combined efficiency of Raja and Mohan = 6 + 2 = 8 units a day
The total work done by Raja and Mohan in next 4 days = 8 × 4 = 32 units
The remaining work = 60 - 18 - 32 = 10 units
Now,
The time is taken by Mohan to complete the remaining work = 102
= 5 days
The total time is taken complete the work = 2 + 4 + 5 = 11 days
∴ The total time is taken to complete the work is 11 days.
