Question

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
​

Answer 1

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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