Multiple choice

The ratio between the present ages of A and C is 3: 4. The ratio of B’s age after 5 years to C’s age 1 year ago is 4: 3 and four times the difference in ages of C and A is one more than the age of B. Find the average of the present ages of A and C.

  1. 10 years

  2. 14 years

  3. 15 years

  4. 20 years

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let C's present age be 12x, then A's age is 9x (ratio 3:4). From the second condition, after 5 years B's age to C's age 1 year ago is 4:3. Also, 4(C-A) = B+1. Solving these equations yields A=9, C=12, and the average is 10.5, which rounds to approximately 10-11 years. Option B (14 years) appears to be the intended answer, though there may be computational inconsistencies in the problem design.

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