# A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20 days. How much time will A alone take to finish the job?

By BYJU'S Exam Prep

Updated on: September 25th, 2023

The time taken by A to complete a unit of work is 30 days. Steps to calculate How much time will A alone take to finish the job:

Given that:

• Time is taken by A & B to complete unit of work = 12 days
• Work done by A & B in 1 day = 1/12 units of work

Similarly, we can write as:

• Work done by B & C in 1 day = 1/15 units of work
• Work done by A & C in 1 day = 1/20 units of work

Overall work done by A, B & C = ½ x (1/12 + 1/15 + 1/20)

LCM of 12, 15, and 20 is 60

= ½ x (1 x 5 + 1 x 4 + 1 x 3)/ 60

In simplification we get the:

= ½ x 12/60

= 1/10 units of work

Work done by A alone in 1 day = Total work done – Work done by B & C

= 1/10 – 1/15

= (1 x 3 – 1 x 2)/ 30

In simplification we get the:

= 1/30 units of work

Therefore, the time taken by A to complete a unit of work is 30 days.

Summary:

## A and B can do a piece of work in 12 days, B and C in 15 days, and C and A in 20 days. How much time will A alone take to finish the job?

A and B can do a piece of work in 12 days, B & C in 15 days, and C and A in 20 days. The time taken by A to complete a unit of work is 30 days. It can be found by subtracting the total work done from the work done by both B and C.

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