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If the ratio of working efficiency of X and Y is 6 ∶ 5 and that of Y and Z is 5 ∶ 4. If X can complete the work in 4 days, then in how many days the total work will be completed if X and Y are assisted by Z on every alternate day?1. 21/11 days2. 3 days3. 28/15 days4. 2 days |
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Answer» Correct Answer - Option 3 : 28/15 days Given: Ratio of work efficiency of X and Y is 6 ∶ 5 and that of Y and Z is 5 ∶ 4. X can complete the work in 4 days. Z assists X and Y on every alternate day. Concepts used: Time = Work/Efficiency Efficiency = Work/Time Work = Efficiency × Time Calculation: Ratio of work efficiency of X and Y is 6 ∶ 5 and that of Y and Z is 5 ∶ 4. X ∶ Y = 6 ∶ 5 Y ∶ Z = 5 ∶ 4 ⇒ X ∶ Y ∶ Z = 6 ∶ 5 ∶ 4 X can complete the work in 4 days. Work = Efficiency × Time Total work done by X = 6 × 4 = 24 unit Time = Work/Efficiency First day work of X and Y = 6 + 5 = 11 unit Remaining work = 24 – 11 = 13 unit Second day work of X, Y and Z = 6 + 5 + 4 = 15 unit 15 unit work is done by X, Y and Z in 1 day. Time taken by X, Y and Z to complete 13 unit work = 13/15 Total time taken by X, Y and Z = 1 day + 13/15 days = 28/15 days ∴ X, Y and Z took 28/15 days to complete the work together if X and Y are assisted by Z on every alternate day. |
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