UGCNET Questions

Let the present ages of the father and son be 7x and 3x respectively. After 10 years, their ages will be 7x + 10 and 3x + 10. The future ratio is (7x + 10) : (3x + 10) = 13 : 7. Cross-multiplying gives 7(7x + 10) = 13(3x + 10), i.e., 49x + 70 = 39x + 130. This simplifies to 10x = 60, so x = 6. Therefore, the father’s present age is 7x = 7 × 6 = 42 years.

Option A:
Option A, 35 years, would make the son 15 years old (ratio 7 : 3), and after 10 years their ages would be 45 and 25, giving a ratio of 9 : 5, not 13 : 7.

Option B:
Option B, 42 years, makes the son 18 years old. After 10 years they would be 52 and 28, and 52 : 28 simplifies to 13 : 7, satisfying both the given present ratio and the future ratio.

Option C:
Option C, 49 years, would imply a son aged 21, and after 10 years their ages become 59 and 31, which do not reduce to 13 : 7.

Option D:
Option D, 56 years, would give the son 24 years at present and 66 and 34 after 10 years, with ratio 33 : 17, again not 13 : 7.

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.