# 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

- Duplicate ratio = a
^{2} : b^{2}
- Sub duplicate ratio = a : b
- Triplicate ratio = a
^{3}: b^{3 }

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

ad = bc

**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

b^{2} = ac

b = ac

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

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