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X and Y together can finish the work in 26 days. If X leaves after 10 days of working, and his place is taken up by Z, Y and Z finish the remaining work in 16 days. Find the time taken by Z to finish the work alone, if X is three times as efficient as Y.1. 35(2/3) days2. 34(2/3) days3. 34(1/3) days4. 32(1/3) days5. 32(2/3) days |
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Answer» Correct Answer - Option 2 : 34(2/3) days Given: X and Y finish work together in 26 days. X leaves after 10 days. Y and Z finish the remaining work in 16 days. The ratio of efficiency of X and Y = 3 ∶ 1 Concept used: Work = Time × Efficiency Calculation: Total work done by X and Y = (1x + 3x) × 26 = 104x Let the efficiency of Z be ‘z’. Total work = (1x + 3x) × 10 + (1x + z) × 16 ⇒ 104x = 40x + (1x + z) × 16 ⇒ 1x + z = 4x Or, efficiency of Z = 3x Time is taken by Z to finish the work alone = 104x/3x = 34(2/3) days. ∴ Z will take 34(2/3) days to finish the work. |
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