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Question
A and B can do a piece of work in 12 days, while B and C can do it in 15 days where as A and C can do it in 20 days. How long would each take to do the same work?
Solution
(A + B) complete the work in 12 days.
∴ (A + B)’s 1 day work = `1/12` ...(1)
(B + C) complete the work in 15 days
∴ (B + C)’s 1 day work = `1/15` ...(2)
(A + C) complete the work in 20 days
∴ (A + C)’s 1 day work = `1/20` ...(3)
Now (1) + (2) + (3) =
[(A + B) + (B + C) + (A + C)]’s 1 day work = `1/12 + 1/15 + 1/20`
(2A + 2B + 2C)’s 1 day work = `5/60 + 4/60 + 3/60`
2(A + B + C)’s 1 day work = `(5 + 4 + 3)/60`
| 5 | 12, 15, 20 |
| 4 | 12, 3, 4 |
| 3 | 3, 3, 1 |
| 1, 1, 1 |
L.C.M = 5 × 4 × 3 = 60
(A + B + C)’s 1 day work = `12/(60 xx 2)`
(A + B + C)’s 1 day work = `1/10`
Now A’s 1 day’s work = (A + B + C)’s 1 day work – (B + C)’s 1 day work
= `1/10 - 1/15`
= `3/30 - 2/30`
= `1/30`
∴ A takes 30 days to complete the work.
B’s 1 day work – (A + B + C)’s 1 day’s work – (A + C)’s 1 day’s work
= `1/10 - 1/20`
= `6/60 - 3/60`
= `(6 - 3)/60`
= `3/60`
= `1/20`
B takes 20 days to complete the work.
C’s 1 day work (A + B + C)’s 1 day work – (A + B)’s 1 day work
= `1/10 - 1/12`
= `6/60 - 5/60`
= `(6 - 5)/60`
= `1/60`
∴ C takes 60 days to complete the work.
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