A can do a piece of work in 30 days,b in 50 days and c in 40 days.if a is assisted by b on one day and by c on the next dayalternately work will be completed in.
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Answer:
18 days
Step-by-step explanation:
A can do a piece of work in 30 days
∴ Work completed by A in one day = 1/30
similarly,
work done by B in one day = 1/50
& work done by C in one day = 1/40
On 1st day, a and b are working togather.
∴ Work completed by a and b togater (ab) = 1/30 + 1/50 = 8/150 = 4/75
when a and c areworking togather,work completed = (ac) = 1/30 + 1/40
∴ ac = 7/120
∴ in two days, work completed = ab + ac = 4/75 + 7/120 = 1/5(4/15 + 7/24)
ab + ac = 1/5 × [(96+105)/360]
∴ ab + ac = 201 / 1800 .... (1)
∴ in 2 days, 201/1800 of work will be completed.
at this rate, number of days required to complete the work = 2 × (1800 / 201)
∴ Number of days to complete the work = 2 × 8.9 = 17.9 ≈ 18
∴ Number of days to complete the work = 18 days
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