Ananya's piggy bank holds only Rs 5 coins and Rs 2 coins. There are 60 coins in all and their total value is Rs 204. How many Rs 5 coins are there?

Let there be $x$ coins of Rs 5 and $y$ of Rs 2. $x+y=60$ and $5x+2y=204$. Substituting $y=60-x:5x+120-2x=204$, so $3x=84$ and $x=28$, giving $y=32$. Check: 28 + 32 = 60 and 140 + 64 = 204. 32 is the number of Rs 2 coins, the swapped unknown; 34 comes from dividing Rs 204 by Rs 6, as if the coins came in equal pairs; 26 fails both checks $(26\times 5+34\times 2=198)$.