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A and B can finish a job in 6 and 8 days respectively. After 2 days of working together, they started to work the alternating way in which A starts first. Find the time in which total work is completed.1. 4 days2. \(4\frac{3}{4}\) days3. 5 days4. \(5\frac{3}{4}\) days5. 3 days |
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Answer» Correct Answer - Option 2 : \(4\frac{3}{4}\) days Given: A and B can finish a job in 6 and 8 days respectively They worked together for 2 days Calculation A can complete the work in 6 days B can complete the work in 8 days Let the total work be LCM of (6, 8) = 24 units Efficiency of A = 24/6 = 4 units Efficiency of B = 24/8 = 3 units Work done by A and B in 2 days = 2 × (4 + 3) = 14 units Remaining work = 24 – 14 = 10 units Now, they started working together starting with A ⇒ Work done by A on day 1 = 4 units ⇒ Work done by B on day 2 = 3 units Remaining work done by B on day = 3/4 units Total work will be completed in = 2 + 1 + 1 + (3/4) ⇒ \(4\frac{3}{4}\) days ∴ Time taken to complete total work is \(4\frac{3}{4}\) days |
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