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      Question

      The average age of a group of 70 students is

      14 years. If three students whose ages are 22 years, 20years, ________ years are replaced with three new students whose ages are 19 years, ______ years, and 32 years, then the new average age is increased by 0.4 years. The value given in the option, which of the following will correctly fill the banks.┬а I. 17, 36┬а II. 22, 41┬а III. 15, 34┬а
      A Only I Correct Answer Incorrect Answer
      B Only II, III Correct Answer Incorrect Answer
      C Only I, III Correct Answer Incorrect Answer
      D Only I, II Correct Answer Incorrect Answer
      E All I, II, III Correct Answer Incorrect Answer

      Solution

      The average age increased by 0.4 years . ┬а So, the difference of sum of ages of new student to the age of old student = 70*0.4 = 28 years ┬а (19+32+__x___) - (20+22+__y_ _) = 28 ┬а (x-y) + (51 -4 2 ) = 28┬а ┬а x-y = 19┬а ┬а So, option I, II, and III all satisfy the above relation┬а ┬а Hence, all three will be the answer

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