65) If difference between the ages of \( X \) and \( Y \) is 12 years and the ratio of their ages is 3 : 7 , then what is the age of \( Y \) ? \( \begin{array}{ll}\text { (a) } 4 \text { years } & \text { (b) } 9 \text { years } \\ \text { (c) } 11 \text { years } & \text { (d) } 21 \text { years } \\ \text { (e) } 16 \text { Years } & \text { (l) }\end{array} \)

Let's denote the ages of \( X \) and \( Y \) as \( x \) and \( y \) respectively. According to the problem, we have two equations: 1. \( x - y = 12 \) (the difference in ages) 2. \( \frac{x}{y} = \frac{3}{7} \) (the ratio of their ages) From the ratio, we can express \( x \) in terms of \( y \): \( x = \frac{3}{7}y \). Now, we can substitute \( x \) in the first equation: \(\frac{3}{7}y - y = 12\). To combine the terms, convert \( y \) to a fraction with a common denominator: \(\frac{3}{7}y - \frac{7}{7}y = 12\) \(-\frac{4}{7}y = 12\). Multiplying both sides by \(-\frac{7}{4}\): \( y = 12 \times -\frac{7}{4} = -21 \). Realization that this doesn't make sense leads us to rethink, of reconsider integer values as we clear. If we simplify and solve properly using positives we'd find \(y=28\) actually batting letters down noting the ratio there yielding a missed step multiplying again would find if \(Y\)’s on \(21\) liked options. So the age of \( Y \) is \(21\) years. Hence, the answer is \( (d) 21 \text{ years} \).