Finding the ratio of two quantities

Finding the ratio of two quantities

The ratio of two quantities can be calculated using the following steps:

1. Express the given quantities A and B in ratio form, that is, A : B.
2. Add the given quantities, that is, A + B.
3. Write the ratio of the given quantities to the sum of all quantities in fraction, that is, A/A + B and B/A + B.
4. If you are given another quantity, for example C, multiply each proportion by the given quantity C: A/A + B × C and B/A + B × C.

The answers in step 4 are the values of each quantity in the ratio of quantities A and B, respectively, with the given share C.

Example 1

Two villages shared a revenue of 16,000,000 shillings in the ratio of 2 : 3. How much did each village get?

Solution

The ratio of the villages is as follows:

(First village) : (Second village) = 2 : 3

Add the ratios: 2 + 3 = 5.

The total revenue for all villages = 16,000,000 shillings

Divide the revenue as follows:

The first village: $2/5$ × sh 16,000,000 = sh 6,400,000.

The second village: $3/5$ × sh 16,000,000 = sh 9,600,000.

Therefore, the first village got 6,400,000 shillings and the second village got 9,600,000 shillings.

Example 2

Asha bought shares for 600,000 shillings in a cooperative shop. She divided the share to her two children, Juma and Halima in the ratio of 5 : 7. How much money did each child get?

Solution

Arrange the ratio of Juma to Halima as follows:

Juma : Halima = 5 : 7

Add the ratios: 5 + 7 = 12

The total share = 600,000 shillings

Calculate the amount of money that each child got as follows:

Juma: $5/12$ × sh 600,000 = sh 250,000

Halima: $7/12$ × sh 600,000 = sh 350,000.

Therefore, Juma got 250,000 shillings and Halima got 350,000 shillings.

Example 3

If A : B = 2 : 3, find the value of:

(a) B if A = 30

(b) A if B = 1,050

Solution

(a) Write A : B = 2 : 3 in fraction:

That is, $A/B = 2/3$.

To find the value of B, substitute A = 30 in the above fraction:

$30/B = 2/3$.

Cross-multiply as follows:

$2 × B = 3 × 30$

$2B = 90$.

Divide both sides by 2:

$2B/2 = 90/2$

$B = 90/2 = 45$.

Therefore, B = 45.

(b) Write A : B = 2 : 3 in fraction:

That is, $A/B = 2/3$.

To find the value of A, substitute B = 1,050 in the above fraction:

$A/1050 = 2/3$

Cross-multiply as follows:

$3 × A = 2 × 1050$

$3A = 2100$.

Divide both sides by 3:

$3A/3 = 2100/3$

$A = 2100/3 = 700$.

Therefore, A = 700.