At a museum, 3 adult tickets and 4 child tickets cost Rs 380, while 2 adult tickets and 5 child tickets cost Rs 335. Find the price (in Rs) of one child ticket.

Let an adult ticket cost Rs $x$ and a child ticket Rs $y.3x+4y=380$ and $2x+5y=335$. Multiplying the first by 2 and the second by 3: $6x+8y=760$ and $6x+15y=1005$. Subtracting: $7y=245$, so $y=35$ and $x=80$. Check: $2\times 80+5\times 35=160+175=335$. 80 is the adult ticket, the wrong unknown; 45 is just the difference between the two bills; 115 is one adult plus one child ticket.