Question
βAβ and βBβ alone can do a certain work in 30
days and 40 days, respectively. Both started the work together but after βxβ days βAβ left the work and the rest work was completed by B alone in β2xβ days. Find the total time taken to complete the whole work in this way.Solution
Total work = 120 units (LCM of 30 and 40) Efficiency of βAβ = 120/30 = 4 units/day Efficiency of βBβ = 120/40 = 3 units/day According to the question, βAβ worked for βxβ days and βBβ worked for β2x days. Therefore, (4+3)x + 3 Γ 2x = 120 Or 7x + 6x = 120 Or x = 120/13 total time taken to complete the whole work = 3Γ120/13 =360/13 days =27.69days
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