**PERCENTAGES SHORTCUTS FOR QUANTITATIVE APTITUDE**

1. " Percent " implies " for every hundred".

2.The base used for the sake of percentage change calculations is always the original quantity unless otherwise stated.

3. In general, if the percentage increase is p%, then the new value is [(p/100) +1]

4. If the new value is k times the old value, then the percentage increase is (k-1) x 100

Eg1: If the percentage increase is 300%, the new value is 4
times the old value.

If the new value is 4 times the old value, the percentage increase is 300%.

5. If there are successive increases of p%, q% and r% in three stages, the effective percentage increase is

= {[(100+p) /100] [(100+q)/100] [ (100+r)/100] -1} x 100

Eg2: The percentage increase in the value of exports of apples of a country is as follows:

2001- 2002 => 25 %; 2002-2003 => 20 %; 2003-2004 => 10%

What is the percentage increase in the value of exports of apples of the country from 2001 to 2004?

Ans : Let the value of exports in 2001 be 100 units.

Then total
percentage increase is:

= {[(100+25)/100] [ (100+ 20)/ 100] [ (100+10)/100] - 1} x 100

= {(1.25) (1.20) (1.10) -1} x 100

= [1.65-1.00] x 100

= [0.65] x 100

= 65

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6. If the price of an item goes up by x %, the percentage reduction required to bring it down to the original price is:

= {100x / (100+x)} %

Eg3:
If the price of an item goes up by 10%, by what percentage should the
new price be reduced to bring it down to the original price?

Ans: Percentage reduction = {100 x 10/ (100 + 10)} %

= (1000/110) %

= 9.09 %

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7.
If the price of an item goes down by x %, the percentage increase
required to bring it back to the original price = {(100 x 10) / (100 -
x)} %.

8. If A is x % more/ less than B, then B is {(100 x 10) / (100 - x)} % less/ more than A.

9.
If the price of an item goes up by x %, then the quantity consumed
should be reduced by {100x /(100 +x)} % so that the total expenditure
remains the same.

10. If the
price of an item goes downs by x %, then the quantity consumed should be
increased by {100x /(100 -x)} % so that the total expenditure remains
the same.

Eg4: If the price of
tea goes up by 10%, then what should be the percentage decrease in the
quantity consumed so that the total expenditure on tea remains the same?

Ans: Required Percentage decrease = { (10 x 100) / (100+10) }%

= (1000/110) %

= 9.09%

11. If A's income is x% more than that of B, then B's income is less than that of A by [(100r)/(100+r).

12. If B's income is x% less than that of A, then A's income is more that of B by [(100x)/(100-x)]

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