PROPORTION –
An equality of two ratios is called a proportion. Four non-zero quantities a, b, c, & d are said to be in proportion if a : b = c : d and we write a : b : : c : d (we write it as ‘a’ is to ‘b’ as ‘c’ is to ‘d’)
If, a : b : : c : d, then;
(i) a, b, c, d are known as first, second, third, and fourth term respectively.
(ii) d is called the fourth proportional to a, b, c.
(iii) a & d are called extremes, while b & c are called means.
Extremes Means
------------ = -----------
Means Extremes
a c
------- = -------
b d
An important property –
If a : b : : c : d, then the product of extremes is equal to the product of means.
Proof- a : b : : c : d
a c
=> ------ = ------
b d
=> ad = bc
So, product of extremes = product of means
Third Proportional -
If, a : b = b : c, then c is called the third proportional to a & b
Clearly, it is the fourth proportional to a, b, c.
Example) If, x : 10 : : 8 : 5, find the value of x
Ans.) Given, x : 6 : : 8 : 5
So, as per the rules –
=> x : 10 = 8 : 5
x 8
=> ------- = ------
10 5
8 X 10
=> x = ---------- = 16
5
So, the desired value of ‘x’ is 16. (Ans.)
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