Continued Proportion

Quantities are said to be in continued proportion if the first is related to the second, the second is related to the third and the third is related to the forth and so on.

If a,b,c,d,e are in continued proportion then

\frac{{\text{a}}}{{\text{b}}} = \frac{{\text{b}}}{{\text{c}}} =  \frac{{\text{c}}}{{\text{d}}} = \frac{{\text{d}}}{{\text{e}}}

Example:
Three persons A, B and C earned a profit of 70000 Rs in a business. Their share in profit is as follows
A : B = 4 : 2
B : C = 10 : 5
Find share of each person.
Solution:
Total amount of profit = 70000
Ratio of A, B and C is

\underline {\begin{array}{*{20}{c}} {\text{A}}&{\text{:}}&{\text{B}}&{\text{:}}&{\text{C}} \\ {\text{4}}&{\text{:}}&{\text{2}}&{}&{} \\ {}&{}&{{\text{10}}}&{\text{:}}&{\text{5}} \end{array}}


\underline {\begin{array}{*{20}{c}} {40}&:&{20}&:&{10} \end{array}}


Sum of ratio = 40 + 20 + 10 = 70

Share of A = \frac{{40}}{{70}}x 70000 = 40000

Share of B = \frac{{20}}{{70}}x 70000 = 20000

Share of C = \frac{{10}}{{70}}x 70000 = 10000
Example:
Divide 2562 among the three friends X, Y and Z. Such that ratio between their shares as
X : Y = 4 : 5
Y : Z = 8 : 10
Solution:
Let amount to be divide = 2562
Ratio of their share

\underline  {\begin{array}{*{20}{c}} {\text{X}}&{\text{:}}&{\text{Y}}&{\text{:}}&{\text{Z}} \\ {\text{4}}&{\text{:}}&{\text{5}}&{}&{} \\ {}&{}&{\text{8}}&{\text{:}}&{{\text{10}}} \end{array}}


\underline  {\begin{array}{*{20}{c}} {32}&{}&:&{}&{40}&{}&:&{}&{50} \end{array}}


Sum of ratios = 32 + 40 + 50 + 122

Share of X = \frac{{32}}{{122}}x 2562 = 672

Share of Y = \frac{{40}}{{122}}x 2562 = 840

Share of Z = \frac{{50}}{{122}}x 2562 = 1052

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