Ajit can do as much work in 2 days as Baljit can do in 3 days and Balj...
Given information:
- Ajit can do as much work in 2 days as Baljit can do in 3 days
- Baljit can do as much in 4 days as Diljit in 5 days
- All three work together for 20 days to complete a piece of work
To find:
- How long would Baljit take to do all the work by himself?
Solution:
Let's start by finding the efficiency of each person, i.e., how much work each person can do in one day.
Let efficiency of Baljit be x.
Efficiency of Ajit = (2/3)x (as he can do the same work as Baljit in 2 days, which means his efficiency is 1/2 of Baljit's efficiency)
Efficiency of Diljit = (4/5)x (as he can do the same work as Baljit in 4 days, which means his efficiency is 4/5 of Baljit's efficiency)
Now, we know that when all three work together, they complete a piece of work in 20 days. So, the total work done in 20 days is:
20[(2/3)x + x + (4/5)x] = 1 (as they complete the whole work)
Simplifying the above equation, we get:
x = 1/44
This means Baljit's efficiency is 1/44 of the total work in a day.
To find how long Baljit will take to do all the work by himself, we can use the formula:
Time taken = Total work / Efficiency
Total work = 1 (as Baljit has to do the whole work by himself)
Efficiency of Baljit = x = 1/44
Substituting these values in the formula, we get:
Time taken = 1 / (1/44) = 44 days
Therefore, Baljit will take 44 days to do all the work by himself.
Answer: Option (c) 66 days