Ratio and Proportion set 1

RATIO AND PROPORTION

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The concept of ratio & proportion is an important for the aptitude exams like Bank PO & CRT exams. Questions based on this topic have asked individually or in data interpretation question set.

Ratio:

The ratio of number x to a number y is defined as

x / y

Some Important Posts:

• Percentage:
• SBI
• IBPS
• RBI

Important properties of ratio –

1. If we multiply the numerator & the denominator of a ratio by the same number ,the ratio remain unchanged

That is

2. If we divide the numerator & the denominator of a ratio by the same number ,the ratio remain unchanged

That is

3. Two or more than two ratio compared by equating the denominators of the ratios & then compared the numerators of the ratios.

If   &  thenwhich is greater than we have to equating both the denominator than compare

it is know that

4. The ratio of two fractions can be expressed as a ratio of two integers

:  =

5. The multiplication of two ratios is as

=

6. If       =  =  =  then

       =

7. If we have two equation of three variables then we cannot find any value of variables but with the help of ratio we can find the proportion between them is

Then       :  :

8. If three quantities a ,b & c in proportion then  then
9. If , then ad = bc and  (Alternando)
10. If     (Componendo and dividendo)
11. If  are four unequal numbers, then  lies between minimum and maximum of all these ratios.

VARIATION:

Two quantities A and B are said to be varying with each other if there exists some relationship between A and B such that the change in A and B is uniform and governed by some rule.

Some typical examples of variation

1. Area of a square is , hence area of a square is directly proportional to .
2. If the number of men on a project is doubled, the number of days will be halved. This shows indirect variation.
3. Expenses of a hostel are partly constant and partly vary with the number of occupants.

Direct proportion :

A varies directly to B, and then A is said to be in direct proportion to B. It is written as

A   or A = kB

It can be understood with the typical example of percentage relating to expenses, consumption and price of the article. If A is directly proportional to B, it simply means that the ratio   is constant. If A becomes double, B also become double; if A is reduced to one third, then B is also reduced to one third etc. Now suppose A is proportional to , it means

A = k or the ratio of A and ,  is constant.

Now take a different case, suppose z is directly proportional to x, when y is constant and directly proportional to ,, when x is constant, then

z x   when y is constant and

z  , when x is  constant

Combining both the relations, we get,

z x

Inverse variation:

If A is inversely proportional to B, it can be written as:

A

A = , where k is a constant.

Joint or mixed variation:

If C is a quantity which is partly constant and partly varies with n, then

C = A + Bn

Where A and B are constant.