Question
Mukta takes 8 hours less than Raj to complete the work,
and Mukta also takes 32 hours less than Bheem to complete the same work. If Raj and Bheem start working together and the time taken by them to complete the work is same as the time taken by Mukta alone to complete the work, then what will be the time taken by Mukta and Bheem to complete the given work.Solution
Let the number of days taken by Mukta to complete the work be “x”. Number of days taken by Raj = (x + 8) Number of days taken by Bheem = (x + 32) 1/(x + 8) + 1/(x + 32) = 1/x 2x2 + 40x = x2 + 40x + 256 2x2 - x2 = 256 x2 = 256 or x = 16 Number of days taken by Mukta = 16 days Number of days taken by Bheem = 48 days Let the total work be 48 units. Mukta’s one-day work = 3 units Bheem’s one-day work = 1 unit Required time = 48/4 = 12 days
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