Three years ago, Rashmi was thrice as old as Nazma. Ten years later, Rashmi will be twice as old as Nazma. How old are Rashmi and Nazma now?

Let present age of Rashmi and Nazma be \(\displaystyle x\) years and \(\displaystyle y\) years respectively. Therefore, \(\displaystyle x-3=3(y-3)\) \[\text { or } \quad x-3 y+6=0 \] and \[x+10=2(y+10) \] or \[x-2 y-10=0 \] Solving equations to get \(\displaystyle x=42, y=16\) ∴ Present age of Rashmi is $\displaystyle 42$ years and that of Nazma is $\displaystyle 16$ years.