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      Question

      The values given in which of the following options will

      fill the blanks in the same order in which it is given to make the statement true: Five years hence, the age of ‘H’ will be 14 years. Present age of ‘G’ is 5/3 of the present age of ‘H’. Present ages of ‘A’, ‘B’, ‘C’, ‘D’, ‘E’ and ‘F’ are in the form of ‘4p’, ‘5p’, ‘q’, ‘2q’, ‘3r’ and ‘4r’ years respectively. If the sum of present ages of ‘A’ and ‘E’ is ____ years, difference between present ages of ‘B’ and ‘D’ is ____ years, and average present age of ‘C’ and ‘F’ is ____ years, then average present age of all the given persons is ____ years. I. 34, 8, 15, 15 II. 35, 9, 14, 18 III. 30, 6, 10, 16
      A Both I and III Correct Answer Incorrect Answer
      B Only III Correct Answer Incorrect Answer
      C Only II Correct Answer Incorrect Answer
      D Both I and II Correct Answer Incorrect Answer
      E Both II and III Correct Answer Incorrect Answer

      Solution

      Present age of 'H' = 14 - 5 = 9 years Present age of 'G' = (5/3) X 9 = 15 years Statement I: Let the present age of 'A', 'B', 'C', 'D', 'E' and 'F' be '4p', '5p', 'q', '2q', '3r' and '4r' years respectively. 4p + 3r = 34 -------- (I) 5p - 2q = 8 -------- (II) (q + 4r) ÷ 2 = 15 q + 4r = 30 --------- (III) On solving equation II + 2 X equation III, 5p - 2q + 2 X (q + 4r) = 8 + 2 X 30 Or, 5p - 2q + 2q + 8r = 8 + 60 Or, 5p + 8r = 68 -------- (IV) On solving 5 X equation I - 4 X equation IV, We get, 5 X (4p + 3r) - 4 X (5p + 8r) = 5 X 34 - 4 X 68 Or, 20p + 15r - 20p - 32r = 170 - 272 Or, 17r = 102 Or, 'r' = 6 On putting value of 'r' in equation I, We get, 4p + 3 X 6 = 34 Or, 4p = 16 Or, 'p' = 4 On putting value of 'r' in equation III, We get, q + 4 X 6 = 30 Or, 'q' = 6 Average present age of all the given person= (4p + 5p + q + 2q + 3r + 4r + 15 + 9) ÷ 8 = (9 X 4 + 3 X 6 + 7 X 6 + 24) ÷ 8 = (120/8) = 15 years So, statement I is true. Statement II: Let the present age of 'A', 'B', 'C', 'D', 'E' and 'F' be '4p', '5p', 'q', '2q', '3r' and '4r' years respectively. 4p + 3r = 35 -------- (I) 5p - 2q = 9 -------- (II) (q + 4r) ÷ 2 = 14 q + 4r = 28 --------- (III) On solving equation II + 2 X equation III, 5p - 2q + 2 X (q + 4r) = 9 + 2 X 28 Or, 5p - 2q + 2q + 8r = 9 + 56 Or, 5p + 8r = 65 -------- (IV) On solving 5 X equation I - 4 X equation IV, We get, 5 X (4p + 3r) - 4 X (5p + 8r) = 5 X 35 - 4 X 65 Or, 20p + 15r - 20p - 32r = 175 - 260 Or, 17r = 85 Or, 'r' = 5 On putting value of 'r' in equation I, We get, 4p + 3 X 5 = 35 Or, 4p = 20 Or, 'p' = 5 On putting value of 'r' in equation III, We get, q + 4 X 5 = 28 Or, 'q' = 8 Average present age of all the given person= (4p + 5p + q + 2q + 3r + 4r + 15 + 9) ÷ 8 = (9 X 5 + 3 X 8 + 7 X 5 + 24) ÷ 8 = (128/8) = 16 years So, statement II is false. Statement III: Let the present age of 'A', 'B', 'C', 'D', 'E' and 'F' be '4p', '5p', 'q', '2q', '3r' and '4r' years respectively. 4p + 3r = 30 -------- (I) 5p - 2q = 6 -------- (II) (q + 4r) ÷ 2 = 10 q + 4r = 20 --------- (III) On solving equation II + 2 X equation III, 5p - 2q + 2 X (q + 4r) = 6 + 2 X 20 Or, 5p - 2q + 2q + 8r = 6 + 40 Or, 5p + 8r = 46 -------- (IV) On solving 5 X equation I - 4 X equation IV, We get, 5 X (4p + 3r) - 4 X (5p + 8r) = 5 X 30 - 4 X 46 Or, 20p + 15r - 20p - 32r = 150 - 184 Or, 17r = 34 Or, 'r' = 2 On putting value of 'r' in equation I, We get, 4p + 3 X 2 = 30 Or, 4p = 24 Or, 'p' = 6 On putting value of 'r' in equation III, We get, q + 4 X 2 = 20 Or, 'q' = 12 Average present age of all the given person= (4p + 5p + q + 2q + 3r + 4r + 15 + 9) ÷ 8 = (9 X 6 + 3 X 12 + 7 X 2 + 24) ÷ 8 = (128/8) = 16 years So, statement III is true. Hence, option a.

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