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      Question

      Three numbers are given, where one-third of the first

      number, two-fifths of the second number, and three-fourths of the third number are all equal. The difference between the second and third numbers is 98. Determine the average of the first and third numbers.
      A 172 Correct Answer Incorrect Answer
      B 166 Correct Answer Incorrect Answer
      C 194 Correct Answer Incorrect Answer
      D 182 Correct Answer Incorrect Answer

      Solution

      Let the three numbers be 'a', 'b' and 'c' respectively.

      ATQ, (a/3) = (2b/5) = (3c/4) = 'k'

      So, 'a' = 3k, 'b' = (5k/2) and 'c' = (4k/3)

      Now, (5k/2) - (4k/3) = 98

      Or, (7k/6) = 98

      So, 'k' = 84

      Therefore, required average = (1/2) X {3k + (4k/3) }

      = (1/2) X (13k/3) = (13k/6)

      = (13 X 84) ÷ 6 = 182

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