Examples of Uses of Ratio and Continued Ratio

Example:
A profit of Rs. 8920 is to be divided among four people in the ratios 5 : 9 : 11 : 15 respectively. How much does each partner get?

Solution:

Given Profit = 8920
Ratio between shares = 5 : 9 : 11 : 15
Sum of ratios = 5 + 9 + 11 + 15 = 40

1st Partner’s Share = \frac{5}{{40}} x 8920 = 1115
2nd Partner’s Share = \frac{9}{{40}} x 8920 = 2007
3rd Partner’s Share = \frac{{11}}{{40}} x 8920 = 2453
4th Partner’s Share = \frac{{15}}{{40}} x 8920 = 3345

Example:
A, B and C starts business with Rs. 5000 for 1 year, Rs. 6000 for 9 months and Rs. 3000 for 7 months. They earned a profit of RS. 3375. Find the share for each.

Solution:
Let the total profit = 3375

Ratio of investments

\begin{array}{*{20}{c}} A&:&B&:&C \\ {5000}&:&{6000}&:&{3000} \\ 5&:&6&:&3 \end{array}

Ratio between their periods

\begin{array}{*{20}{c}} {12{\text{ months}}}&{\text{:}}&{{\text{9 months}}}&{\text{:}}&{{\text{7 months}}} \\ {{\text{12}}}&{\text{:}}&{\text{9}}&{\text{:}}&{\text{7}} \end{array}

Ratio of investments with respect to time

\begin{array}{*{20}{c}} {5{\text{ x 12}}}&{\text{:}}&{{\text{6 x 9}}}&{\text{:}}&{{\text{3 x 7}}} \\ {{\text{60}}}&{\text{:}}&{{\text{54}}}&{\text{:}}&{{\text{21}}} \\ {{\text{20}}}&{\text{:}}&{{\text{18}}}&{\text{:}}&{\text{7}} \end{array}

Sum of ratios = 20 + 18 + 7 = 45

Share of A = \frac{{20}}{{45}} x 3375 = 1500
Share of B = \frac{{18}}{{45}} x 3375 = 1350
Share of C = \frac{7}{{45}} x 3375 = 525