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M can complete a work in 10 days working 7 hours a day. N can complete the same work in 6 days working 10 hours a day. If both M and N work together, working 8 hours a day, in approx how many days can they complete the work?

M can complete a work in 10 days working 7 hours a day. N can complete the same work in 6 days working 10 hours a day. If both M and N work together, working 8 hours a day, in approx how many days can they complete the work? Correct Answer None of the above

Time taken by M to complete a work = 10 × 7 = 70 hours

Work M can do in 1 hour = 1/70

Time taken by N to complete the same work = 6 × 10 = 60 hours

Work N can do in 1 hour = 1/60

Work M and N can do in 1 hr = 1/70 + 1/60 = 130/4200 = 13/420

Hours taken by M and N to complete the work = 420/13

If they work 8 hrs per day, days required to complete the work = 420/(13 × 8) = 4.04 ≈ 4 days

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