Tricks of percentage

1. If x is a% more than y, then y is  [{ a/(100+a)}× 100]% less than x.

2. If x is a% less than y, then y is [{a/(100-a)}× 100]%  more than x.

Q. If income of Ravi is 20% more than that of Ram, then income of Ram is how much per cent less than that of Ravi?
EXPLANATION
Here a =20%
According to the formula,
   Required percentage = [{a/(100+a)}× 100] %
                                          = [{20/(100+20}×100]%
                                          = 50/3 %

Q. If in an examination, the marks obtained by Preeti is 20% less than that of Vandana, then marks obtained by Vandana is how much per cent more than marks obtained by Preeti?
EXPLANATION
Here a = 20%
According to the formula,
      Required percentage = [{a/(100-a)} ×100] %
                                             = [{20/(100-20)} × 100] %
                                             = 25%

 Tricks of Percentage set-1

3. If the price of a commodity increases or decreases by a%, then the decrease or increase in consumption, so as not to increase or decrease the expenditure equal to 
[{a/(100±a)} ×100] %

Q. If the price of a commodity be raised by 40%, by how much per cent must a householder reduce his consumption of that commodity, so as not to increase his expenditure?
EXPLANATION 
Here a = 40%
According to the formula, 
      Reduction to consumption = [{40/(100+40)}×100] %
                                                      = (40/140)×100%
                                                      = 200/7 %

4. The passing marks in an examination is P%. If a candidate scores R marks and fails by F marks, then
 Maximum marks, M = 100 × (R+F) /P

Q. A student has to score 30% marks to get through. If he gets 30 marks and fails by 30 marks, then find the maximum marks set for the examination.
EXPLANATION 
Here R = 30, F = 30, P = 30
According to the formula,
    Maximum marks = 100 × ( 30 + 30)/30
                
5. If due to r% decrease in the price of an item, a person can buy A kg more in x. then
Actual price of that item = r x/ {(100- r) × A} 

Q. If due to 10% decrease in the price of sugar, Ram can buy 5 kg more sugar in ? 100, then find the find actual price of sugar.
EXPLANATION
  Here r = 10%, x = 100, A =5
Therefore actual price of sugar = 10× 100 /{ ( 100- 10) × 5}
                                                          = 1000 / 450
                                                          = 2.22

6. If two candidates contested in an election and one candidate got x% of total votes casted and still lose by y votes, then
 Total number of votes casted = 100 × y /( 100 - 2x)

Q. In an election contested by two candidates, one candidate got 30% of total votes and still lost by 500 votes, then find the total number of votes casted.
EXPLANATION
Here x = 30, y = 500
Therefore total number of votes = 100y/(100-2x)
                                        = 100× 500/( 100 - 2× 30)
                                        = 1250

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