Percentage

ð  Percentage

First of all remember these %-ratio  relation, this will help in solving ques:

100 %     = 1

  50 %     = 1/2

33.33 % = 1/3

      25 % = 1/4

      20 % = 1/5

16.66 % = 1/6

14.28 % = 1/7

12.50 % = 1/8

11.11 % = 1/9

      10 % = 1/10

Now three methods are there to solve the % problems:

1-      Increase-Decrease

2-      Successive Change

3-      Multiplying Factor

Increase-Decrease

Ø  It deals with ratio, if a objects is increasing with 25%=1/4 then it will be decrease by 20%=1/5 or if an object is decreasing with 25%=1/4 then it will be increase by 33.33%=1/3.

Ø  One more example if increasing by 75%=3/4, then decrease with 3/7.

Ø  And if decrease with 2/5, then increase with 2/7.

Ø  So, as per above examples we can see, if something is increasing with a/b, then it will bw decreasing with a/(b-a) and if decreasing with a/b then increase with a/(a+b)

This concept can solve many types of questions just like:

Ques 1- If area of a land is remains same and we are increasing the length by 25%, then how much % changes required in the width?

Ans 1- A= L x B, where A constant. So, A/L=B (means L and B are inversely proportional)

So if L increases, B decreases

Hence, if L is increased by 1/4 then B should be decreased by 1/5 .

Ques 2- If speed is decreased by 25% then how much more time needed to complete a particular distance?

Ans 2- Speed= Distance/Time, where Distance is constant.

So if Speed decreases, Time increases

Hence, if Speed is decreased by 1/4 then Time should be increased by 1/3 .

Ques 3- If rates of a commodity increased by 50% then what will be the effect on its consumption as per Indian market trend?

Ans 3- As per Indian market trend, Rates & Consumption are inversely proportional to each-other.

So if Rates increases Consumption decreases

Hence, if rate is increased by 1/2 then consumption should be decreased by 1/3 .

Successive change

Ø  Unit A----x%---Unit B----y%----Unit C

Then overall changes from A to C is S.C.= x+y+xy/100

If profit/increase/surcharge, then value is (+) positive

If loss/decrease/discount, then value is (-) negative

Ø  Rmember these combination represent x%, y%, S,C. %

+20 , +25 -> +50

+25 ,  -20 -> 0

 -25 , +20 -> -10

This concept can solve many types of questions just like:

Ques 1- If length of a rectangle is increased by 20% and width by 25%, then how much % changes occurs in area?

Ans 1- 20+25+20*25/100= 50 %

Multiplying Factor

           

Ø  A------x%-----B-------y%------C-------z%--------D

Then overall change from A to D=a*mf1*mf2*mf3= A*(1+x/100)*(1+y/100)*(1+z/100)

So mf1=1+x/100

This concept can solve many types of questions just like:

Ques 1- Current population=3 lakh,If population of a country increases by 10% every year, then what is the population after 3 years?

Ans 1- mf= 1_10/100= 1.1

So overall population= 3*1.1*1.1*1.1= 3.993 lakh

Conclusion- If a problem deals with only one time percentage change, Increase/Decrease trick is useful.

If there are two times changes in percentage, then Successive Change trick is good.

And if there are more than two times percentage changes exist, use Multiplying factor.

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