Unit 1C

1. In a shop the ratio of the number of motor cycles to the number of scooters is 7 : 3. Given that there are 45 scooters in the shop, calculate the number of motor cycles.

2. Hotel expenses, totalling £185.90, account for 65% of the cost of a holiday. Calculate the total cost of the holiday.

3. In a batch of 150 articles 6% were defective. Calculate the number which were not defective.

4. Express 1.26 metres as a percentage of 4.5 metres.

5. A map is drawn to a scale of 1 : 50 000.

(a) Calculate the actual distance, in kilometres, represented by 1 cm on the map.

(b) Two towns are 24 km apart. Calculate, in centimetres, their distance apart on the map.

(c) On the map, a farm has an area of 20 cm². Calculate, in square kilometres, the actual area of the farm.

6. In a quadrilateral PQRS, the angles P, Q and R are in the ratio 1 : 4 : 8 and their sum is 273°. Find (a) S, (b) R.

7. A scale model of a church is made. The ground area of the model is one hundredth of the actual ground area.

(a) Given that the length of the model is 4 m, calculate the length of the church.

(b) Given that the volume of the church spire is 3000 m³, calculate the volume of the spire on the model.

8. Given that 5 cm on a map represents 4 km on the ground,

(a) calculate the distance, in km, between two villages which are represented on the map by points 7.5 cm apart,

(b) express the scale of the map in the form 1 : n,

(c) calculate, in cm², the area of the map which represents a region of area 48 km² on the ground.

9. A bag contains counters of three different colours. Given that ³⁄₁₀ of them are red counters, ¹⁄₈ of them are green counters and the remaining counters are yellow, calculate

(a) the fraction of counters which are yellow,

(b) the percentage of counters which are green,

(c) the smallest possible number of counters in the bag.

10. Find 15% of $10.80.