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Two friends X and Y started typing work and were hopeful to complete the work in 10 days and 15 days respectively. They started the work together, but due to an emergency, X left after just 5 days and asked his friend Z to join at his place, who could alone complete this work in 60 days. In how many days did the work get completed?1. 142. 63. 74. 5 |
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Answer» Correct Answer - Option 3 : 7 Given: Time taken by X to complete the work alone = 10 days Time taken by Y to complete the work alone = 15 days Time taken by Z to complete the work alone = 60 days Formula Used: Efficiency = Total work/Time taken Calculation: Let the total work be 60x units (LCM of 10,15, 60) Efficiency of X = 6x units/day Efficiency of Y = 4x units/day Efficiency of Z = x units/day Work done in 5 days by X and Y = (6x + 4x) × 5 = 50x units ⇒ Remaining work = 60x – 50x = 10x units This work is completed by Y and Z Time taken to complete the remaining work = 10x/[(4x + x)] = 10x/5x = 2 days Total time taken to complete the whole work = 5 + 2 = 7 days ∴ The total time taken to complete the whole work is 7 days |
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