A and B can do a piece of work in 40 days B and C in 30 days and C and A in 24 days.

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asked May 15 in Class VIII Maths by priya12 (-12,269 points)

A and B can do a piece of work in 40 days; B and C in 30 days; and C and A in 24 days.
(i) How long will it take them to do the work together ?
(ii) In what time can each finish it working alone ?

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1 Answer

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answered May 15 by navnit40 (-4,290 points)
A and B can do a piece of work in = 40 days
B and C can do a piece of work in = 30 days
C and A can do a piece of work in = 24 days
(A+B)’s 1 day work = 1/40
(B+C)’s 1 day work = 1/30
(C+A)’s 1 day work = 1/24
(i) [(A+B)+(B+C)+(C+A)]’s 1 day work =  1/40 + 1/30 + 1/24

= (3 + 4 + 5)/120

= 12/120 = 1/10

i.e. (A + B + B + C + C + A)’s 1 day work = 1/10

i.e. 2(A + B + C)’s 1 day work = 1/10

∴ (A + B + C)’s 1 day work = 1/10 × ½

= 1/20

∴ (A + B + C) can do the work in = 20 days

(ii) A’s 1 day work = 1/20 – 1/30

= (3 – 2)/60 = 1/60

∴ A can do the work in 60 days

B’s 1 day work = 1/20 – 1/24

= (6 – 5)/120 = 1/120

∴ B can do the work in 120 days

Now, C’s 1 day work = 1/20 – 1/40

= (2 – 1)/40 = 1/40

C can do the work in 40 days
Hence A can do the work in = 60 days
B can do the work in = 120 days
C can do the work in = 40 days

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