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      Question

      The present ages of R and S are in the ratio 5:6. 3 years

      back, the average age of R, S, and T was 33 years. R was 12 years younger than T at that time. What will be T’s age 7 years from now?
      A 45 yrs Correct Answer Incorrect Answer
      B 32 yrs Correct Answer Incorrect Answer
      C 55 yrs Correct Answer Incorrect Answer
      D 49 yrs Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      Let current ages be: R = 5x, S = 6x, T = y

      3 years ago: 5x–3, 6x–3, y–3

      ATQ,

      (5x–3 + 6x–3 + y–3) = 3 × 33

      ⇒ 11x + y – 9 = 99

      ⇒ 11x + y = 108 ---------- (I)

      Also,

      5x – 3 = y – 3 – 12

      ⇒ 5x = y – 12

      ⇒ y – 5x = 12 ---------- (II)

      Subtracting (II) from (I):

      11x + y – (y – 5x) = 108 – 12

      ⇒ 16x = 96

      ⇒ x = 6

      Then y = 5x + 12 = 30 + 12 = 42

      ∴ T’s age after 7 years = 42 + 7 = 49 years

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