Six years ago Kavita was four times as old as her nephew. The sum of their present ages is 47 years. Find the nephew's present age.

Let Kavita be $x$ and the nephew $y$ years old now. $x+y=47$ and $x-6=4(y-6)$, that is $x-4y=-18$. Subtracting gives $5y=65$, so $y=13$ and $x=34$. Check: 34 + 13 = 47, and six years ago $28=4\times 7$. 34 years is Kavita's age, not the nephew's; 7 years is the nephew's age six years ago, not now; 28 years is Kavita's age six years ago.