### PEA 305 HAND WRITTEN NOTES with SOLUTIONS(Percentage,S.I ,C.I, FRACTION)

Pea 305

*For Ratio and Alligation Go Down. \/*

**Hand written Notes with Question-Amswer**

**And complete Solution**

In Ca2 These may help a lot So Guys Have Look on this <°_°>

PERCENTAGE

A percentage is a ratio expressed in terms of a

unit being 100. A percentage is usually

denoted by the symbol “%”.

To express a% as a fraction, divide it by 100

⇒ a% = a/100

To express a fraction as %, multiply it by 100

⇒ a/b = [(a/b) × 100] %

x% of y is given by (y × x/100 )

Point to remember for faster Calculation

1 = 100% 1 /2= 50%

1 /3= 33.33% 1/4 = 25%

1/5 = 20% 1 /6= 16.66%

1/7 = 14.28% 1/8 = 12.5%

1/9 = 11.11% 1/10 = 10%

1/11 = 9.09% 1/12 = 8.33%

Some Short tricks based on Condition

If A's income is r% more than B's income, the

B's income is less than A's income by

[ r / (100+r)] * 100%

If A‟s income is r% less than B‟s income, the

B‟s income is more than A‟s income by

[ r / (100-r)] * 100%

If 'A' is x% of 'C' and 'B' is y% of 'C' then 'A' is

(x/y) * 100% of 'B'.

If the sides of the triangle, rectangle, square,

circle, rhombus etc is

(i) Increased by x%. Then its area is increased

by 2x+(x2 /100)

(ii) If decreased by x%. Then its areas is

decreased by, -2x+(x2 /100)

If a number x is successively changed by a%,

b%, c%. then final value

x (1+a/100) (1+b/100) (1+c/100)

The net change after two successive changes

of a% and b% is

(𝐫 𝐫𝐵/100) %

The population of a town is 'P'. It increased by

x% during 1st year, increased by y% during

2nd year and again increased by z% during

3rd year. Then the population after 3 years

will be,

P * [(100+x)/100] * [(100+y)/100] * [

(100+z)/100 ]

Mixture problems

If x% of a quantity is taken by the first

person, y% of the remaining quantity is taken

by the second person, and z% of the

remaining is taken by the third person and if

A is left, then initial quantity was

A/(1-x%)(1-y%)(1-z%)

The same concept we can use, if we add

something, then the initial quantity was

A/(1+x%)(1+y%)(1+z%)

**For Hand Written Notes:: CseNotes12**

**For Ratio and Alligation Mcqs:: CseNotes12**

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