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Pecentage Calculation

We can use the following shortcuts for calculating percentages:
  1. Convert the percentage to fractions: For example, if we want to find 12.5% of 124. We can solve this as given below –
     
    12.5% of 124
     
    = > 1/8 of 124
     
    = > 15.5 Ans
Use the following table for doing conversions of percentage to fraction:
 
= 100% = 50% = 33.33% = 25% = 20%
= 16.67% = 14.28% = 12.5% = 11.11% = 10%
 
  1. Break the percentage into small parts: Suppose you want to find 51% of 128. This can be found in a very easy way, as given below –
     
    51% of 128
     
    ⇒ (50% + 1%) of 128
     
    ⇒ 64 + 1.28
     
    ⇒ 65.28
  2. Interchange the number and percentage: Suppose, we have to find 39% of 12.5. This will be equal to 12.5% of 39. So, we instead of finding 39% of 12.5, we can find 12.5 % of 39, which will be equal to 1/8*39 (as 12.5% is equal to 1/8).
For solving complex problems of percentages, we can use a mix of above three shortcut approaches.

Some Important Conclusions

  • if A is a% more than B then B is less than A by
  • if A is a% less than B then B is more than A by
  • if A number is increased by a% then decreased by a% then net change will be
  • if a number is increased or decreased successively by a% and b% then net change is %
  • if a number is first time increased by a% and then decreased by b% then net change is %
  • if a number is increased successively by a%, b% and c% then net change is
  • if in an examination a% of the student failed in one subject, b% failed in another subject and c% failed in both subject then the percentage of student who
    1. failed in either of subject = a + b - c
    2. passed in both subject = 100 - (a + b - c)

Percentage Increase/Decrease

If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
 
If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:

Results on Population

Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
  1. Population after n years = 
  2. Population n years ago = 

Results on Depreciation

Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
  1. Value of the machine after n years = 
  2. Value of the machine n years ago =       
  3. If A is R% more than B, then B is less than A by
  4. If A is R% less than B, then B is more than A by




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