# CLASS-10RATION & PROPORTION - INTRODUCTION OF PROPORTION

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

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.)