A courier company charges a fixed booking fee for a parcel plus a rate for every kilogram it weighs. A 5 kg parcel costs Rs 410 and an 8 kg parcel costs Rs 590. Find the rate (in Rs) charged per kilogram.

Let the booking fee be Rs $x$ and the rate Rs $y$ per kg. $x+5y=410$ and $x+8y=590$. Subtracting: $3y=180$, so $y=60$ and $x=410-300=110$. Check: $110+8\times 60=590$. 110 is the booking fee, the other unknown; 82 comes from dividing the whole 5 kg charge by 5, which wrongly spreads the booking fee over the weight; 180 is the difference between the two charges before dividing by the 3 kg.