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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
Table of content
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.
