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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