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A alone can complete a work in 20 days and B alone can complete the work in 30 days while C alone can complete work in 60 days. If A and B work on the first day and B and C work on the second day then how much time will it take for A, B and C together to complete the work after 2nd day?

A alone can complete a work in 20 days and B alone can complete the work in 30 days while C alone can complete work in 60 days. If A and B work on the first day and B and C work on the second day then how much time will it take for A, B and C together to complete the work after 2nd day? Correct Answer 26/3 days

Given,

⇒ A’s 1 day’s work = 1/20

⇒ B’s 1 day’s work = 1/30

⇒ C’s 1 day’s work = 1/60

(A + B)’s 1 day’s work = 1/20 + 1/30

= 1/12

(B + C)’s 1 day’s work = 1/30 + 1/60

= 1/20

(A + B + C)’s 1 day’s work

= 1/20 + 1/30 + 1/60

= 1/10

Then,

Total work done till end of 2nd day

= 1/12 + 1/20

= 2/15

Remaining fraction of work

= 1 - 2/15

= 13/15

Total time taken by A, B and C together to complete work

= (13/15) × 10

= 26/3

It will take 26/3 days to complete remaining work.

Alternate Solution:

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The efficiency of (A + B) = 3 + 2 = 5

The efficiency of (B + C) = 2 + 1 = 3

Work done by (B + C) on second day = 3

Remaining work after two days = 60 - 5 - 3 = 52

The efficiency of (A + B + C) = 3 + 2 + 1 = 6

Number of days taken by (A + B + C) to complete the remaining work = 52/6 = 26/3 days

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