Type A man completes a work in 5 days , type B man in 12 days and type C in 40 days. If two men of A type, 3 men of B type and 17 men of C type work collectively, then how much time is required to finish the work?
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Answer:
40/43 of a day
Step-by-step explanation:
Let the work to be completed = W
A can complete the work in = 5 days
B can complete the work in = 12 days
C can complete the work in = 40 days
Amount of work that can be completed in 1 day by A (Wa) = (1/5) W
Amount of work that can be completed in 1 day by B (Wb) = (1/12) W
Amount of work that can be completed in 1 day by C (Wc) = (1/40) W
Men at work:
A type = 2
B type = 3
C type = 17
So, the amount of work that could be done by these men in 1 day at a Rate
= [2 x (1/5)] W + [3 x (1/12)] W + [17 x (1/40)] W
= [(48 + 30 + 51) W] / 120
= (129 /120) W
= (43/40) W
Now,
Amount of Work (W) = Rate x Time
W = (43/40) W x T
=> T = 40/43
Therefore, the time required to finish the work = T = 40/43 of a day
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