#### Rate, ratio and proportion.

1.   Write the following ratios in the simplest form:

38                       42                     52                    136                     247
1.1   ----            1.2   ------            1.3   ----           1.4   ------           1.5   ------
57                     105                     91                    221                     437

2.   Divide
2.1   35 marbles between Peter and John in the ratio 3 : 4.
2.2   R 1 378 between A and B in the ratio 4 : 9.
2.3   R18 214 between A, B and C in the ratio 7 : 5 : 2.
2.4   323,68 between C and D in the ratio 3 : 11.
2.5   96 oxen between P and Q in the ratio 5 : 7.
2.6   364 sheep between R, S and T in the ratio 7 : 4 : 2.

3.   A, B and C buy a shop. They decide to divide the profit in the same ratio as the ratio in which
they contributed to buy the shop. A contributed R120 000, B contributed R100 000 and C contributed
R60 000.
3.1   Write the ratio of their contributions in its simplest form.
3.2   Divide a profit of R48 601 between them.
3.3   C decides to contribute R5 000 of his share to the fund.
3.3.1   Write down the new ratio of their contributions.
3.3.2   The second year the shop shows a profit of R72 917,25. Divide this profit using the new ratio.

4.1   When 24 marbles were divided between John and Mike, John received 9 marbles.
Calculate the ratio in which the marbles were divided.
4.2   An amount of R1 968 was divided between A, B and C. A received R984, B received R615 and
C the rest. Calculate the ratio in which the money was divided.

5.   Increase
5.1   82 kg in the ratio 4 : 5.                     5.2   R735 in the ratio 5 : 9.
5.3   21,7 m in the ratio 7 : 11.                 5.4   28,4 kg in the ratio 4 : 3.
5.5   R324 in the ratio 8 : 5.                     5.6   34,2 litre in the ratio 9 : 5.

6.   The ratio of boys to girls in a class is 8 : 7. There are 45 pupils in the class. How many boys and
how many girls are there in the class?

7.   A class contains 23 boys and 22 girls.
7.1   Write the ratio boys : girls in its simplest form.
7.2   Three boys leave school and thus the class and 4 girls are admitted to the class.
Write down the new ratio b : g.
7.3   The class still contains 23 boys and 22 girls. Pupils leave the school and are admitted to the school
and this class. The total number of pupils in the class is now 44 and the ratio b : g = 6 : 5.
Calculate the number of boys and girls in the class and then say how many boys left
the class or were admitted to the class. Repeat for the girls.

8.   A tin contains red, green and yellow sweets in the ratio r : g : y = 3 : 4 : 5. There are 12 red sweets in
the tin. Calculate the number of green and yellow sweets and the total number of sweets in the tin.

9.   A bag contains 10 kg of 3 : 2 : 1 (22) fertiliser.
9.1   Explain the meaning of the ratio and the 22.
9.2   Calculate the mass of nutrients in the bag.
9.3   Calculate the mass of N of P and K in the bag.

10.   John's father drives at a constant speed of 90 km/h. John takes the time to travel past 5 similar,
equidistant posts. He finds that it takes 16 seconds.
10.1   Show that 90 km/h = 25 m/s.
10.2   Calculate the distance between to consecutive posts.
10.3   When he takes the time again, he finds that it is now 20 seconds. Does the car travel at a higher or
10.4   At what speed does the car travel if the time to move past 5 posts is 12 seconds?
10.5   They now travel past different posts at 90 km/h. The time to pass 5 posts is 24 seconds.
Calculate the distance between 2 consecutive posts.

11.   Calculate the volume of paint needed to cover 20,8 m² if 1 litre of paint covers an area of 5,2 m²

12.   Calculate the area covered by 5,8 litres of paint if 17,6 m² is covered by 2,8 litres of paint.

13.   A tin contains 4,2 litres of paint. 2,5 litres of this paint covers an area of 11,5 m². Will the tin
contain enough paint to cover an area of 21,4 m²? Explain.

14.   A car uses 21,082 litres of petrol to travel 254 km. How much petrol will the car use if
it travels 613 km?

15  A car travels 253,5 km in 2 hours 36 minutes.
15.1   Show that 2 hours 36 minutes is equal to 2,6 hours.
15.2   How far will the car travel in 3 hours and 48 minutes, if it travels at the same speed?
15.3   How long will it take to travel 415 km at the same speed?

16.   Ten men can finish a job in 3 days.
16.1   How long will 7 men take to finish the same job if they work at the same rate?
16.2   How long will 12 men take to finish the same job if they work at the same rate?
16.3   How many men are needed to finish the job in 7 days?
16.4   How many men are needed to finish the job in 2 days?

17.   Twenty children each get 8 sweets from a bottle.
17.1   How many sweets will each child get if there are 40 children?
17.2   How many sweets will each child get if there are 8 children?
17.3   How many children are there if each child gets 16 sweets?
17.4   How many children are there if each child gets 4 sweets?