Ratio and Proportion

Ratio and Proportion


The ratio is a quantity which represents the relationship between two similar quantities.

If the two quantities are a and b, the ratio of a and b represented as a: b or ( a/ b ) Here a is called antecedent and b is called Consequent

Basic Formulas


The ratio of two quantities a and b in the same units is the fraction and we write it as a: b.

Example sum

Divide Rs. 672 in the ratio 5 : 3
Sum of ratio terms = ( 5 +3 )
= 8

First part= Rs. ( 672*(5/8))

= Rs. 420 Second part= Rs. (672 * (3/8))

=Rs. 252

          Types of Ratio

Fourth Proportional

If a : b = c : d, then d is called the fourth proportional to a, b, c.
Example sum

Find the fourth proportion to 2,3,6?
Let the forth proportional 2, 3 and 6 be x.

=>2:3::6:x

=>(2/3)=(6/x)

=> x=18/2 = 9

Third Proportional


a : b = c : d, then c is called the third proportion to a and b.
Example sum
Find the third proportion to 16 and 36?
Let the third proportional 16 and 36 be x.
16: 36 :: 36:x

16*x=36*36

x=(36*36)/16 =81

Comparison of Ratios

We say that (a:b)<(c:d)=>(a/b)>(c/d)
Example sum
1. Find the ratio between 20 and 32?
Ratio = 20 / 32

=5/8

2. Two numbers are in the ratio 3: 5. If 9 is subtracted from each, the new numbers are in the ratio 12: 23. Find a smaller number?
Let the numbers be 3x and 5x.
=> (3x-9)/(5x-9)=(12/23)

23*(3x-9) = 12*(5x-9)

69x – 207=60x – 108

69x – 60x = 207 – 108

9x = 99

x = 11
The smaller number = 3 * 11
= 33