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      Question

      The ratio of age of A and B after 8 years is 4:5

      respectively. The ratio of age of A and C 6 years ago is 3:4 respectively. If the present average age of A and C is 30 years, then find the present age of C.
      A 28.33 years Correct Answer Incorrect Answer
      B 30.22 years Correct Answer Incorrect Answer
      C 32.44 years Correct Answer Incorrect Answer
      D 33.43 years Correct Answer Incorrect Answer
      E None of these Correct Answer Incorrect Answer

      Solution

      ATQ,

      The ratio of A and B's ages after 8 years is 4:5, so we get the equation 5(A+8)=4(B+8), which simplifies to 5A−4B=−8. The ratio of A and C's ages 6 years ago is 3:4, giving us the equation 4(A−6)=3(C−6), which simplifies to 4A−3C=6. The average age of A and C is 30, so A+C=60. Solving the system of equations, we substitute A = 60 − C into the second equation and solve to get C=33.43. Thus, the present age of C is approximately 33.43 years.

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