USING RATIOS TO DIVIDE QUANTITIES

Let us consider the following picture :

In the diagram given above, the ratio of shaded portion to unshaded part is 3 : 2.

There are 5 equal parts.

• In which 3 has been shaded and it can be represented as 3/5
• In which 2 has been unshaded and it can be represented as 2/5.

In the above two quantities the large part is 3/5 of total and small part is 2/5 of total.

Example 1 :

I wish to divide $12000 in the ratio 2 : 3 to give to my children Pam and Sam. How much does each one receive?

Solution :

Total number of parts  =  2 + 3  ==>  5

Out of 5 equal parts Pam will get 2 parts and Sam will get 3 parts.

Amount received by Pam  =  2/5 of 12000

=  (2/5) ⋅ 12000

=  4800

Amount received by Sam  =  3/5 of 12000

=  (3/5) ⋅ 12000

=  7200

Example 2 :

The recommended cordial to water ratio is 1 : 4. Calculate how many mL of cordial are needed to make:

a) a 300 mL glass of mixture

b) a 2L container of mixture.

Solution :

Ratio of cordial to water  =  1 : 4

Total parts  =  1 + 4  ==> 5 parts

Cordial in that mixture  =  1/5 of quantity of mixture

Water in that mixture  =  4/5 of quantity of mixture

(a)  Quantity of cordial  =  1/5 of 300

=  (1/5) ⋅ 300

  =  60 ml

(b)  2 L  =  2000 ml (1 liter  =  1000 ml)

Quantity of cordial  =  1/5 of 2000

=  (1/5) ⋅ 2000

  =  400 ml

Example 3 :

The recommended disinfectant to water ratio is 1 : 20. How many mL of concentrated disinfectant are required to make a 9 L bucket of mixture?

Solution :

Total number of parts  =  1 + 20 ==>  21 parts

Quantity of disinfectant  =  1/21 of mixture

9 L  =  9000 ml

=  (1/21)  ⋅ 9000

=  428.5 ml

Example 4 :

A bag of 25 marble is divided between Jill and John in the ratio 2 : 3.

a)  What fraction does Jill receive?

b) How many marbles does Jill receive?

c) How many marbles does John receive?

Solution :

Total number of parts  =  2 + 3  ==>  5

(a)  Jill will receive 3/5 of marbles

(b)  Amount received by Jill  =  3/5 of 25

=  (3/5) ⋅ 25

=  3(5)

=  15 marbles

(c)  Amount received by John  =  2/5 of 25

=  (2/5) ⋅ 25

=  2(5)

=  10 marbles

Example 5 :

Divide:

a) $20 in the ratio 1 : 4

b) $49 in the ratio 5 : 2.

Solution :

(a)  Total parts  =  1 + 4 ==>  5 parts

One part  =  1/5 of 20

=  (1/5) ⋅ 20

=  4

Second part  =  4/5 of 20

=  (4/5) ⋅ 20

=  16

b) $49 in the ratio 5 : 2.

Total parts  =  5 + 2 ==>  7

One part  =  5/7 of 49

=  (5/7) ⋅ 49

=  35

Second part  =  2/7 of 49

=  (2/7) ⋅ 49

=  14

Example 6 :

$400 is divided in the ratio 3 : 2. What is the larger share?

Solution :

Total parts  =  3 + 2 ==>  5

Larger part  =  3/5 of total

Smaller part  =  2/5 of total

Amount to be divided  =  $400

Larger share  =   (3/5) ⋅ 400

=  240

Example 7 :

$160000 is divided in the ratio 3 : 5. What is the smaller share?

Solution :

Total number of shares  =  3 + 5  ==>  8

Larger share  =  5/8

Smaller share  =  3/8

Amount to be divided  =  $160000

Small share  =  (3/8) ⋅ 160000

=  60000

So, the smaller share is 60000.

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