Friday, September 13, 2019


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 <°_°>

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
The same concept we can use, if we add
something, then the initial quantity was

For Hand Written Notes:: CseNotes12

For Ratio and Alligation Mcqs:: CseNotes12