Let the present ages of A and B be A and B years respectively. We know A + B = 50. After 10 years, their ages will be A + 10 and B + 10, and the ratio (A + 10) : (B + 10) is given as 4 : 3. This gives the equation (A + 10) / (B + 10) = 4 / 3, which can be solved together with A + B = 50. Solving this system yields A = 30 and B = 20, so A’s present age is 30 years.
Option A:
Option A, 20 years, actually corresponds to B’s present age when the system is solved. It reverses the roles of A and B and therefore does not answer the question correctly.
Option B:
Option B, 25 years, would make the sum of their ages 50 only if B were also 25, but this would not satisfy the future ratio of 4 : 3 after 10 years.
Option C:
Option C satisfies both conditions: the present ages 30 and 20 sum to 50, and after 10 years they become 40 and 30, which indeed are in the ratio 4 : 3.
Option D:
Option D, 35 years, would require B to be 15 to keep the sum at 50, and after 10 years the ratio 45 : 25 is not equal to 4 : 3.
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