Question
If Ram works 3 times as fast as Shyam and is able to
complete a work in 40 days less than the number of days taken by Shyam, then find the time (in days) in which they can complete the work, working together.Solution
Let Shyam's time be x days. So, Ram's time is x - 40 days. Since Ram is 3 times faster, Shyam's time is 3 times Ram's time: x = 3(x - 40) x = 3x - 120 => 2x = 120 => x = 60 days (Shyam), Ram's time = 20 days. Ram's 1 day work = 1/20, Shyam's 1 day work = 1/60. Together, 1 day work = 1/20 + 1/60 = (3+1)/60 = 4/60 = 1/15. So, they will complete the work together in 15 days.
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