A bat and a ball cost ₹110 altogether. The bat costs ₹100 more than the ball. What does the ball cost?

If the ball costs $x$, the bat costs $x+100$, so $x+(x+100)=110$, giving $2x=10$ and $x=5$. Checking: the ball is ₹5, the bat is ₹105, the difference is exactly ₹100 and the total is ₹110. The trap is ₹10, the answer almost everyone says first: it comes from splitting off the ₹100 and handing the whole remaining ₹10 to the ball, which makes the bat ₹100 and the gap only ₹90, not ₹100.