The ratio of the ages of Meena and Meera is 4 : 3. The sum of their ages is 28…

When two quantities are given in a ratio a : b, write their actual values as a×x and b×x for some positive constant x; if their sum (or another total) is known, solving the resulting linear equation gives x and hence the real values. Adding the same fixed number of years to two unequal ages does not preserve their original ratio, so a ratio after n years must be computed from the future actual ages, not by editing the ratio terms directly.

1. Let Meena's present age be 4x and Meera's present age be 3x, since their ages are in the ratio 4 : 3.

2. Their sum is 28, so 4x + 3x = 28, i.e., 7x = 28, giving x = 4.

3. So Meena's present age = 4 × 4 = 16 years, and Meera's present age = 3 × 4 = 12 years.

4. After 8 years, Meena's age = 16 + 8 = 24 years and Meera's age = 12 + 8 = 20 years.

5. The ratio of their ages after 8 years = 24 : 20, which simplifies (dividing both terms by 4) to 6 : 5.

Check: the present ages 16 and 12 sum to 28 (matching the given total) and simplify to a ratio of 16 : 12 = 4 : 3 (matching the given ratio), confirming x = 4 is correct. Also, since a constant is added to two unequal ages, the new ratio should move closer to 1 : 1 than before — indeed 6 : 5 (=1.2) is closer to equality than 4 : 3 (≈ 1.33), which is the expected direction of change.