Problems on ratio, rate, proportion, scale drawings, maps


  1. Kelly typed a document at 50 words/min for the first 30 min and at 30 words/min for the next 1 hour until she finished typing the document. Find her average rate of typing the whole document, correct to 1 decimal place.
  2. The petrol consumption of Mr Lim’s car is 8 km per litre. Each week, he has to travel an average distance of 420 km. If petrol is charged at $1.40 per litre, what is Mr Lim’s average weekly petrol bill?
  3. A runner took 2 hr 34 min to finish a 42-km marathon. Assuming that he ran at a constant speed, how long did he take to run 15 km?
  4. A rope is cut into two pieces in the ratio $3:2$. The longer piece is 9.6 m long. Find the length of the shorter piece.
  5. A sum of money is divided in the ratio 4:3. The larger part is $7.20. Find the smaller part.
  6. Express the ratio 700 g to 1.75 kg in its lowest terms. Give your answer in the form $m:n$, where $m$ and $n$ are integers.
  7. A map is drawn to a scale of $1 : 400 \; 000$.
    1. Find the actual distance, in kilometres, represented by 7 centimetres on the map.
    2. A city covers an area of 800 square kilometres. Find, in square centimetres, the area representing the city on the map.