# Uses of Ratio and Continued Ratio

Ratio is used for calculating continued ratio, proportion, rates, and percentage as well as continued proportion. Ratio can also be used to divide profit or amounts between two or more people.

For this we have the following process:

1. First, we find sum of the given ratios.
2. Share can be found with the following formula.

Person’s share= (given amount) (Ratio/Sum of ratios)

Continued Ratio:

So far, we have learnt the method of comparing two quantities of the same kind. But there may be a situation when we have to compare more than two quantities which are in a continued ratio.

Example: Suppose that Rs. 74000 are to be divided among three friends A, B, C, such that
A : B = 4 : 5 and B : C = 3 : 2

$\underline {\begin{array}{*{20}{c}} A&:&B&:&C \\ 4&:&5&{}&{} \\ {}&{}&3&:&2 \end{array}}$
$\begin{array}{*{20}{c}} {12}&:&{15}&:&{10} \end{array}$

Sum of ratio = 12 + 15 + 10 = 37
Share of A = $\frac{{12}}{{37}}$x 74000 = 12 x 2000 = 24000
Share of B = $\frac{{15}}{{37}}$ x 74000 = 15 x 2000 = 30000
Share of C = $\frac{7}{{37}}$ x 74000 = 10 x 2000 = 20000

Example:
Divide 60000 in ratio 5 : 7

Solution:
Let A and B be two people having a ratio of share 5 : 7

Sum of ratios = 5 + 7 = 12
Share of A = $\frac{5}{{12}}$x 60000 = 25000
Share of B = $\frac{7}{{12}}$ x 60000 = 35000

Example:
Three partners invested Rs. 12500, 9000 and 7500 respectively. If the total profit earned  is Rs. 5800, how much profit will each partner receive?

Solution:
Let A, B and C be three partners

A invested = 12500
B invested = 9000
C invested = 7500
Profit = 5800

The ratio among their investments is

$\begin{array}{*{20}{c}} A&:&B&:&C \\ {12500}&:&{9000}&:&{7500} \\ {125}&:&{90}&:&{75} \\ {25}&:&{18}&:&{15} \end{array}$

Sum of ratios = 25 + 18 + 15 = 58
Share of A = $\frac{{25}}{{58}}$ x 5800 = 2500
Share of B = $\frac{{18}}{{58}}$ x 5800 = 1800
Share of C = $\frac{{15}}{{58}}$ x 5800 = 1500