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      Question

      Durgesh can complete a task alone in 21 days. If Vikash

      works alone for 8 days and then leaves, Durgesh can finish the remaining work in 7 days. Satish is 25% less efficient than Durgesh. If Vikash and Satish work together for โ€˜xโ€™ days and then leave, Durgesh can complete the remaining work alone in 6 days. Determine the value of โ€˜xโ€™.
      A 6 Correct Answer Incorrect Answer
      B 7 Correct Answer Incorrect Answer
      C 8 Correct Answer Incorrect Answer
      D 5 Correct Answer Incorrect Answer
      E 4 Correct Answer Incorrect Answer

      Solution

      Answer: A Let the efficiency of Durgesh alone = โ€˜yโ€™ units/day Then, total work = 21 ร— y = โ€˜21yโ€™ units Let the efficiency of Vikash = โ€˜zโ€™ units/day We have, 8 ร— z + 7 ร— y = 21y Or, 8z = 14y So, z:y = 14:8 = 7:4 So, ratio of efficiencies of Vikashย  and Durgesh is 7:4, respectively So, efficiency of Vikash = (7y/4) = โ€˜1.75yโ€™ units/day Efficiency of Satish = y ร— 0.75 = โ€˜0.75yโ€™ units/day Combined efficiency of Vikash and Satish = 1.75y + 0.75y = โ€˜2.5yโ€™ units/day According to the question, 2.5y ร— x + y ร— 6 = 21y Or, 6y + 2.5xy = 21y Or, 2.5xy = 15y So, x = 15 รท 2.5 = 6

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