Question
A and B together can complete a job in 12 days. A alone
can complete it in 20 days. In how many days can B alone complete it? Also, in what ratio should they share Rs 8400 if they are paid proportional to the work they do when working together?Solution
A’s 1-day work = 1/20 (A + B)’s 1-day work = 1/12 So B’s 1-day work = 1/12 − 1/20 LCM(12,20) = 60 1/12 = 5/60, 1/20 = 3/60 So B = (5 − 3)/60 = 2/60 = 1/30 Thus B alone takes 30 days. When working together, their daily work rates: A : B = (1/20) : (1/30) = 30 : 20 = 3 : 2 So they should share the amount in ratio 3 : 2. Share of A = (3/5) × 8400 = 5040 Share of B = (2/5) × 8400 = 3360 Answer: B alone takes 30 days, shares Rs 3360.
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