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A takes 10 days less than the time taken by B to finish a piece of work If both A and B together can finish the work in 12 days the time taken by B to finish the work is |
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Answer» Let B alone finish the work = x days. And Alone finish the work = (x−10) days A' s one day work = 1/x-10 B' s one day work = 1/x As it given the (A + B) can finish work in 12 days ∴ (A + B) one daywork = 1/21 ⇒ A′ some day work + B′ some day work = 1/12 ⇒ \(\frac{1}{x-10}+\frac{1}{x}=\frac{1}{2}\) ⇒ \(\frac{x+x-10}{x(x-10)}=\frac{1}{12}\) ⇒ \(\frac{2x+x-10}{x(x-10)}=\frac{1}{12}\) ⇒ 12(2x−10) = x(x−10) ⇒ 24x − 120 = x2 − 10x ⇒ x2 − 10x − 24x + 120 = 0 ⇒ x2 − 34x + 120 = 0 ⇒ x2 − 30x − 4x + 120 = 0 ⇒ x(x−30) − 4(x−30) = 0 ⇒ (x−4)(x−30) = 0 ⇒ x = 4 or x = 30 x = 4 ∵ if x = 4 then A alone can finish the work in = (4−10) = −6 days which is not possible ∴ x = 30 days |
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