If the ratio of ages of Seema and Reema is 9 : 16, after ten year it will be 2 : 3. The ratio of ages…

Let the present ages of Seema and Reema be $9x$ and $16x$. After 10 years: $\frac{9x + 10}{16x + 10} = \frac{2}{3} \implies 27x + 30 = 32x + 20 \implies 5x = 10 \implies x = 2$. Their present ages are $18$ and $32$ years. Six years ago, the ratio of their ages was $\frac{18 - 6}{32 - 6} = \frac{12}{26} = \frac{6}{13}$, i.e., $6 : 13$.