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A and B together can complete a task in 12 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 25 days in all to complete the work. If B is more efficient than A, how many days would it have taken B to do the work by herself?

A and B together can complete a task in 12 days. However, if A works alone, completes half the job and leaves and then B works alone and completes the rest of the work, it takes 25 days in all to complete the work. If B is more efficient than A, how many days would it have taken B to do the work by herself? Correct Answer 20

Given,

(A + B)’s 1 day’s work = 1/12

⇒ 1/A + 1/B = 1/12

Given,

⇒ (A/2) + (B/2) = 25

⇒ A + B = 50

Solving,

⇒ 1/ (50 – B) + 1/B = 1/12

⇒ B2 – 50B + 600 = 0

⇒ B2 – 30B – 20B + 600 = 0

⇒ B(B – 30) – 20(B – 60) = 0

⇒ B = 30 or B = 20

If B = 30 Then A = 20

If B = 20 Then A = 30

But B is more efficient than A,

∴ B takes 20 days to complete the work.

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