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      Question

      A and B can finish a task together in '2t' days. B alone

      can complete the task in 10 days, while A alone can do it in '5t' days. Find the value of 't'.
      A 5 Correct Answer Incorrect Answer
      B 3 Correct Answer Incorrect Answer
      C 7 Correct Answer Incorrect Answer
      D 1 Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Given: A and B together can do the work in 2t days B alone can do the work in 10 days A alone can do the work in 5t days Their work rates will be A’s rate = 1 / (5t),  B’s rate = 1 / 10 and A + B’s rate = 1 / (2t) Set up the equation A’s rate + B’s rate = (A + B)'s rate So, (1 / 5t) + (1 / 10) = 1 / (2t) Multiply both sides by 10t to eliminate denominators 10t * (1 / 5t) + 10t * (1 / 10) = 10t * (1 / 2t) 2 + t = 5 t = 3

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