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.