Question

A and B can do a piece of work in 12 days.B and C can do a piece of work in 15 days and C and A can do a piece of work in 20 days. how much time take A to finish a job​

Answer 1

Answer:

30 days

Step-by-step explanation:

A and B can do a piece of work in 12 days

So A and B's 1 day work (A + B) = 1/12

B and C can do the same work in 15 days

So B and C's 1 fay work (B + C) = 1/15

C and A can do the same work in 20 days

C and A's 1 day work (C + A) = 1/20

We know that

2(A + B + C) = (A + B) + (B + C) + (C + A)

⇒ 2(A + B + C) = (1/12) + (1/15) + (1/20)

Taking LCM

⇒ 2(A + B + C) = (5 + 4 + 3)/60

⇒ 2(A + B + C) = 12/60

⇒ 2(A + B + C) = 1/5

⇒ A + B + C = (1/5) ÷ 2

⇒ A + B + C = (1/5) × (1/2)

⇒ A + B + C = 1/10

i.e A, B and C's 1 day work = 1/10

We know that

A's 1 day work = A, B and C's 1 day work - B and C's 1 day work

= (1/10) - (1/15)

Taking LCM

= (3 - 2)/30

= 1/30

i.e A's 1 day work = 1/30

So A alone takes 30 days to finish the job.

Hope it may help you .

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