Ram is half of his father age . Twenty years ago the age of father was six times the age of ram.find the age of ram and his father.

$\begin{array}{l}\text{Let the age of Ram father be}\ x\ years\ \\ \text{Hence age of Ram}=\frac{x}{2}\ years\ \\ \text{Age of Ram father 20 years ago }=\left(x-20\right)\ years\ \\ \text{Ram age 20 years ago }=\frac{x}{2}-20\ years\ \\ \text{Hence}\\ x-20=6\left[\frac{x}{2}-20\right]\\ \Rightarrow\ x-20=3x-120\\ \Rightarrow\ 2x=120-20=100\\ \Rightarrow\ x=50\\ \text{Hence Ram father age is }50\ years\ \\ \text{Ram age }\frac{x}{2}=\frac{50}{2}=25\ years\ \end{array}$

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