Ratio and Proportion 2
Proportion and Ratio

When solving problems that contain ratios like 4 : 5 or 3 : 7, it is often useful to write the ratios in the form n : 1 or 1 : m.

So

4 : 5 is equivalent to   1 : or : 1

and

3 : 7 is equivalent to   1 : or : 1.

Worked Examples

1

In a fruit drink, orange juice and pineapple juice are mixed in the ratio 3 : 7. Find how much pineapple juice would be mixed with 500 cm3 of orange juice.

Show me

The ratio of orange juice to pineapple juice is

3 : 7 or 1 :

So for every 1 cm3 of orange juice, cm3 of pineapple juice is needed.

For 500 cm3 of orange juice, the amount of pineapple juice needed is

500 × = cm3
2

Alvin buys 8 m of wire netting to make a rabbit run. This costs him £5.04. Mark is also making a rabbit run. He needs 6.8 m of wire netting. How much will this cost?

Show me The cost per metre of the wire netting is
= 63 p
= 63 p per m

Mark needs 6.8 m. This will cost

6.8 × 63 p = £4.284
= £4.28 (to the nearest p)

This is equivalent to using the ratio 6.8 : 8; so solving this problem as a ratio, you take

× £5.04 = £4.28, to the nearest p (as before).
3

Three men are digging trenches to install cables to connect new houses to the electricity supply. Working together they can dig 12 m of trench each day. Assume the same ratio of productivity in the questions below.

As 3 men dig 12 m each day, 1 man digs 4 m each day.

(a)

How long will it take 2 men to dig 120 m of trench?

Show me

As each man digs 4 m per day, 2 men dig 8 m per day. The time taken to dig 120 m is given by

= 15 days

Alternatively, 2 men can dig

× 12 = 8 m

of trench each day, so it will take

= 15 days

to dig the trench.
(b)

How many men will be needed to dig 80 m of trench in 2 days?

Show me

As each man digs 4 m per day, each man digs 8 m in 2 days, The number of men needed is given by

= 10 men

Exercises

The ratio of the length to width of a photograph is 3 : 2. The photograph is enlarged so that the length is 18 cm.

What is the width of the enlarged photograph?

cm

The ratio of flour to sugar in a recipe is 5 : 4.

(a)

How much flour should be mixed with 100 grams of sugar?

g
(b)

How much sugar should be mixed with 200 grams of flour?

g

The manager of a music store estimates that the ratio of sales of CDs to DVDs is 4 : 7.

(a)

In one day, 92 CDs were sold. How many DVDs were sold that day?

DVDs
(b)

On another day, 84 DVDs were sold. How many CDs were sold that day?

CDs

A 6 m length of rope costs £2.70. Find the cost of the following lengths of rope.

(a)
1 m £
(b)
15 m £
(c)
22 m £

A greengrocer sells sweet potatoes by the kilogram. She sells 5 kg of sweet potatoes for £6.50. Find the cost of:

(a)
7 kg of sweet potatoes, £
(b)
20 kg of sweet potatoes, £
(c)
2 kg of sweet potatoes. £

Mr Plummer employs 5 men who together can build a wall 12 m long in 3 days.
Assume the same ratio of productivity in the questions below.

(a)

How long would it take the men to build a wall 20 m long?

days
(b)

How long would it take 3 men to build the 12 m wall?

days
(c)

If the 12 m wall must be built in 2 days, how many more men must Mr Plummer employ?

men

A school with 700 pupils employs 25 teachers. Use this ratio of teachers and pupils to answer the following questions.

(a)

How many teachers are needed for a school of 560 pupils?

teachers
(b)

How many pupils are there in a school with 22 teachers?

teachers
(a)

An orange drink is made by mixing water with orange syrup.

of the orange drink is water.

How many litres of water will be in 12 litres of orange drink?

litres
(b)

It takes 100 g of flour to make 15 shortbread biscuits.

(i)

Calculate the weight of flour needed to make 24 shortbread biscuits.

g
(ii)

How many shortbread biscuits can be made from 1 kg of flour?

biscuits