A, B and C can complete a work in 20 days, 15 days and 12 days, respectively. They all started the work together, but C left the job 3 days before its completion, and B left the job 2 days before C. In how many days, did the work get completed ?

Given:

A can complete a work in 20 days.

B can complete a work in 15 days.

C can complete a work in 12 days.

C left the job 3 days before its completion.

B left the job 2 days before C.

Formula Used:

Work done by A in 1 day = 1/20

Work done by B in 1 day = 1/15

Work done by C in 1 day = 1/12

Total work = 1

Calculation:

Let the total number of days to complete the work be x.

Since C left 3 days before completion, C worked for (x - 3) days.

Since B left 2 days before C, B worked for (x - 5) days.

A worked for x days.

Work done by A in x days = x × 1/20

Work done by B in (x - 5) days = (x - 5) × 1/15

Work done by C in (x - 3) days = (x - 3) × 1/12

Total work done = Work done by A + Work done by B + Work done by C

⇒ x/20 + (x - 5)/15 + (x - 3)/12 = 1

⇒ x/20 + (x - 5)/15 + (x - 3)/12 = 1

⇒ (3x + 4(x - 5) + 5(x - 3))/60 = 1

⇒ (3x + 4x - 20 + 5x - 15)/60 = 1

⇒ (12x - 35)/60 = 1

⇒ 12x - 35 = 60

⇒ 12x = 95

⇒ x = 95/12

⇒ x = 7(11/12)

The work gets completed in 7(11/12) days.