How to solve problem related to Ratios and Proportions

Ratio: The ratio of two quantities a and b in the same units is the form a/b and we write its as a:b

Proportion: The equality of two rations is called proportion. If a:b = c:d, we write as a:b::c:d and we say that a,b,c,d are in proportion.

Example1: If a:b=2:3, and b:c=5:6, then the value of a:b:c?
Solutions:

Given that a:b=2:3 and
                 b:c=5:6
To solve this type of problem easily write numbers as given below

Number of variables in ration:           a        b          c
 Their values                                    2        3
                                                                  5         6                         
                            a:b:c  = (ab:bb:bc) = (2x5):(3x5):(3x6) = 10:15:18
Note:
1. In Ratios and Proportions the final answer will vary, if the ratio is canceled by single number then cancel it.   
2. If three rations a:b, b:c, c:d are given then a:b:c:d can be calculated as abc:bbc:bcc:bcd

Example 2:  What number must be added to each term of the ration 7:11 so as to make it equal to 3:4.

The terms of the ration 7:11 are 7 and 11
let  'x' be the number to be added to these terms so as to make it equal to 3:4, then we can write as

7+x:11+x = 3:4

7+x           3
-----  =  -----
11+x         4

4(7+x) = 3(11+x) => 28+4x = 33+3x => 4x-3x = 33-28 => x=5.

There the number to be added is 5.

Note: If two numbers are in the ration a:b, then we take as: the two terms are 'a' and 'b', the two numbers are 'ax' and 'bx'.