Uses of Ratio and Continued Ratio

Ratio is used for calculating continued ratio, proportion, rates, percentage as well as continued proportion. Ratio can also be used for dividing the profit or amount between two or more people.
For this we have the following process:

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

Share of a person= (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 the situation when we have to compare more than two quantities, which are in a continued ratio.
For 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 persons having 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  Rs. 5800, how much profit each partner will receive.
Solution:
Let A, B and C be three partners
A invested = 12500
B invested = 9000
C invested = 7500
Profit = 5800
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

Comments

comments