# Aptitude ratio and proportion

Ratio is the comparison of two or more elements of same type in simple terms.

The ratio of a to b is written as a:b (or) a/b and read as 'a is to b'.

Example :

If the amounts with A and B are 20 lakhs and 10 lakhs respectively, we say that A has twice or double that of B.

The number of times one quantity contains other quantity is called ratio of two quantities.

In a: b the first element is called antecedent and second element is called consequent.

Ratio can be modified by multiplying or dividing its terms with the same number.

1 : 2 = 2( 1 : 2) =2 : 4

1 : 2 = 3(1 : 2) = 3 : 6

i.e., 1/2 = 2/4 = 3/6 = 3: 6

If a: b is the ratio then

1. Duplicate ratio = a2 : b2
2. Sub duplicate ratio = a : b
3. Triplicate ratio = a3: b3

If a : b, c : d and e: f are three ratios then compound ratio = ratio of first elements to second elements in all the ratios

i.e., a* c* e: b *d * f

If two ratios a : b and c : d are equal then we say that the proportionals a, b, c and d are in proportion

a:b=c:d [written as a : b : : c : d]

a/b = c/d

Product of extremes is equal to product of means.

Here 'a' and 'd' are called 'extremes' and 'b' and 'c are called 'means'.

If a, b, c are in continued proportion then

a:b=b:c

b2 = ac

b = ac

Here 'b' is called Mean proportional of 'a' and 'c'.