Concept of 'BY' and 'TO' Percentage

Concept of 'BY' and 'TO' Percentage

Please note that there is a clear difference between "by" and "to" e.g., the income is reduced by 40% it means the new income is 60% of the original and the income is reduced to 40% means the new income is 40% of the original value.  Thus "by" represents difference and "to" represents final value.

e.g., The income of sarika is increased by 20% means its new income is 100+20 = 120% of the original income. The income of sarika is increased to 120% means the new income of sarika is 120% of the original income.

Example 1: 

In an election between two candidates, the candidate who got 57% valid notes won by a majority of 420 votes. Find the total no. of valid votes.

Solution:

winner                          loser

0.57x                             0.43x                                   (100-57=43)

       -----------------------                                            (57-43 = 14)

                 0.14x

0.14x = 420

x = 3000

Hence total valid votes = 3000