InterviewSolution
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A is 25% more efficient then B. A works for ‘D’ days and completed 1/3 of work and left the work and remaining work is completed by B in ‘D + 12’ day. In how many days A and B together can complete the work.1). 15 days2). \(13\frac{1}{3}days\)3). 12 days4). \(12\frac{1}{3}days\) |
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Answer» A works for D days and completed 1/3rd of WORK Work done by A in D days = 1/3 A alone can complete the work = 3D days Work done by A in 1 day = (1/3) × (1/D) = 1/3D Ratio of time taken by A and B = 100 : 125 Let’s assume B alone can complete the work in in x days. ⇒ 100 / 125 = 3D/x ⇒ x = 15D/4 Remaining work = 1 - 1/3 = 2/3 2/3rd of work completed by B in (D + 12) days. ⇒ 2/3 = (4/15D) × (D + 12) ⇒ 30D = 12D + 144 ⇒ 18D = 144 ⇒ D = 8 A can alone complete the work in 8 × 3 = 24 days B alone can complete the work in = 15/4 × 8 = 30 If A and B work TOGETHER, work will be completed in = 1/[(1/24) + (1/30)] = 1/(9/120) = 120/9 ∴ A and B together complete the work in 120/9 = $(13\frac{1}{3})$ Days |
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