varun can do a work alone and takes 8 more days than rahul alone . Rahul is 50%less efficient than arun. If all 3 together can do a same piece of work in 30 days then find the time taken by arun alone?
Answers
Given:
varun can do a work alone and takes 8 more days than rahul alone . Rahul is 50%less efficient than arun. If all 3 together can do a same piece of work in 30 days
To find:
Find the time taken by arun alone.
Solution:
From given, we have,
varun can do a work alone and takes 8 more days than rahul alone.
Let the total number of days rahul takes to complete the work be = x days.
Therefore, the total number of days varun takes to complete the work = (x + 8) days
Rahul is 50%less efficient than arun.
This implies that, Rahul = 50% of Arun
x/50% = Arun
⇒ Arun = x/(50/100) = 100x/50 = 2x
Therefore, the total number of days arun takes to complete the work = 2x days
It's given that, all 3 together can do a same piece of work in 30 days
⇒ x + (x + 8) + 2x = 30
⇒ 4x + 8 = 30
⇒ 4x = 30 - 8 = 22
⇒ x = 22/4
⇒ x = 5.5
Then, the time taken by arun alone is calculated as follows.
the total number of days arun takes to complete the work = 2x days
= 2 × 5.5
= 11 days.
Thus, Arun takes 11 days to complete work alone.