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      Question

      'X' can complete 75% of a work in 15 days, whereas 'Y' can

      complete 25% of the same work in 10 days. They both started working together, but 'Y' left the job 'n' days before the work finished. If the entire work is completed in 14 days, then find the value of [0.6n + (n²/5)].
      A 6 Correct Answer Incorrect Answer
      B 1 Correct Answer Incorrect Answer
      C 2 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Time taken by 'X' to complete the entire work = (15/75) × 100 = 20 days

      Time taken by 'Y' to complete the entire work = (10/25) × 100 = 40 days

      Let the total work be 40 units (LCM of 20 and 40)

      Efficiency of 'X' = 40/20 = 2 units/day

      Efficiency of 'Y' = 40/40 = 1 unit/day

      ATQ:

      (2 × 14) + [1 × (14 - n)] = 40

      28 + (14 - n) = 40

      42 - n = 40

      n = 2

      Required value = 0.6n + (n²/5) = (0.6 × 2) + {(2 × 2)/5} = 1.2 + 0.8 = 2

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