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A and B can do a piece of work in 18 days; B and C in 24 days and A and C in 36days. In what time can they do it, all working together?

Answer:

Every task necessitates a specific amount of time and a specific workforce, or the number of individuals who will complete the task.

Work is usually categorised as a "1" unit. This time and and work concept is a follow-up to direct and inverse proportion.

The given details are,

A and B can do a piece of work in = 18 days

Work done by A and B in 1 day = 1/18

B and C can do a piece of work in = 24 days

Work done by B and C in 1 day = 1/24

A and C can do a piece of work in = 36 days

Work done by A and C in 1 day = 1/36

By adding A, B and C we get,

2(A+B+C) one day work = 1/18 + 1/24 + 1/36

= (4+3+2)/72 (by taking LCM for 18, 24 and 36 which is 72)

= 9/72

= 1/8

A+B+C one day work = 1/(8×2) = 1/16

∴ A, B and C together can finish the work in = 1/(1/16) = 16days.

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