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Question

‘A’ and ‘B’ alone can do a certain work in 30 days and 40 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.

A 28days Correct Answer Incorrect Answer
B 12days Correct Answer Incorrect Answer
C 24days Correct Answer Incorrect Answer
D 48days Correct Answer Incorrect Answer

Solution

Total work = 120 units (LCM of 30 and 40) Efficiency of ‘A’ = 120/30 = 4 units/day Efficiency of ‘B’ = 120/40 = 3 units/day According to the question, ‘A’ worked for ‘x’ days and ‘B’ worked for ‘2x days. Therefore, 4x + 3 × 2x = 120 Or 4x + 6x = 120 Or x = 120/10 = 12 total time taken to complete the whole work = 2×12=24days

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