IT A and B can do a work in 60 days and 40 days. If C joins after 3 days can do the
same work in 30 days, then the number of days to
days, then the number of days taken to complete the work if they work together
Answers
A, B and C can complete the work together in 12 days.
Given:
A and B can do work in 60 days and 40 days
If C joins after 3 days can do the same work in 30 days
To find:
The number of days taken to complete the work if they work together
Solution:
Given that
A can do a work in 60 days
=> The work done by A in 1 day = 1/60
B can do the same work in 40 days
=> The work done by B in 1 day = 1/40
Given that C joined after 3 days this means
A and B worked for 3 days
C can complete the work in 30 days
The work done by C in 1 day = 1/30
Let x be number of days the three of them completed the work
Then the work done by A, B and C = 1
=> x [ 1/60 + 1/40] + (x-3)[1/30] = 1
=> x/24 + (x-3)/30 = 1
=> [ 5x + 4x - 12 ]/120 = 1 [ take 120 as LCM ]
=> [ 9x - 12 ] = 120
=> 9x = 108
=> x = 108/9
=> x = 12
Therefore,
A, B and C can complete the work together in 12 days.
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