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A and B separately can build a wall in 12 and 16 days, respectively. If they work for 1 day alternatively, starting with A, in how many days will the wall be built?1. \(7{2\ \over3}\) days2. \(13{2\ \over3}\) days3. \(12{2\ \over3}\) days4. \(6{2\ \over3}\) days |
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Answer» Correct Answer - Option 2 : \(13{2\ \over3}\) days Given : A can do a work in 12 days B can do the same work in 16 days They work on alternate days Concept used : work done each day = total work/total number of days Calculations : Total work = LCM of 12 and 16 ⇒ 48 units A's per day work = 48/12 = 4 units B's per day work = 48/16 = 3 units Total work done in 13 days (7 days of A and 6 days of B) = 7 × 4 + 6 × 3 = 46 units Remaining work = 48 – 46 = 2 units Time taken by B to complete the remaining work = 2/3 (B's turn to do the work) ⇒ 2/3 days Total time taken = 13 + 2/3 ⇒ \(13{2\ \over3}\) days ∴ Total \(13{2\ \over3}\) days will be taken to complete the work |
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