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A, B and C can do a work separately in 20, 35 and 60 days, respectively. They started the work together, but B and C left 8 days and 12 day, respectively, before the completion of the work. In how many days will the work be completed?

A, B and C can do a work separately in 20, 35 and 60 days, respectively. They started the work together, but B and C left 8 days and 12 day, respectively, before the completion of the work. In how many days will the work be completed? Correct Answer 15 days

Given:

Time taken by A = 20 days

Time taken by B = 35 days

Time taken by C = 60 days

B and C left 8 days and 12 days

Formula used:

Work = Time × Efficiency

Calculation:

LCM of 20, 35 and 60 is 420

Efficiency of A = (420/20) = 21

Efficiency of B = (420/35) = 12

Efficiency of C = (420/60) = 7

Now,

Suppose B and C does not leave till the work get completed

Work of B and C for 8 days and 12 days = (12 × 8 + 7 × 12) 

⇒ (96 + 84)

⇒ 180 

New total work = (420 + 180) = 600 

Number of days to complete the whole work by A, B and C = Total work/Efficiency of (A + B + C)

⇒

⇒ 600/40

⇒ 15 days

∴ The required days is 15 days

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