Question
A’ and ‘B’ alone can do a certain work in 20 days
and 30 days, respectively. Both started the work together but after ‘x’ days ‘A’ left the work and the rest work was completed by B alone in ‘2x’ days. Find the total time taken to complete the whole work in this way.Solution
Total work = 60 units (LCM of 20 and 30) Efficiency of ‘A’ = 60/20 = 3 units/day Efficiency of ‘B’ = 60/30 = 2 units/day According to the question, ‘A’ worked for ‘x’ days and ‘B’ worked for ‘2x days. Therefore, 3x + 2 × 2x = 120 Or 3x + 4x = 60 Or x = 60/7days total time taken to complete the whole work = 2×60/7=120/7days
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