Percentage
Points to Remember1) Y % is expressed as  Y 
100 
2) To find percent of  x  =   x  × 100   % 
y  y 
Quick Tips and Tricks 1. Prices of Goods (1) If the price of goods increases by R %, then the
reduction in consumption so as not to
increase the expenditure can be calculated using the formula:
 R  × 100   % 
(100 + R) 
(2) If the price of goods decreases by R %, then the increase in consumption so as not to decrease the expenditure can be calculated using the formula:
 R  × 100   % 
(100 – R) 
2. Numerical on Population: Population of a city at present is P and it increases at the rate of R% per annum.
(1) To find population after n years = P   1 +  R   ^{n} 
100 
 (After n years population increases, thus   1 +  R   is used) 
100 
(2) To find population n years ago =  
P 
 1 +  R   ^{n}  100 

3. Numerical on Depreciation: Present value of machine is M, If it depreciates at the rate of R% per annum.
(1) To find value of machine after n years = P   1 –  R   ^{n} 
100 
 (After n years the value of machine decreases, thus   1 –  R   is used) 
100 
(2) To find the value of machine n years ago =  
P 
 1 –  R   ^{n}  100 

Question VarietyGenerally 5 types of questions are asked from this chapter. Understanding these concepts will help in solving the problems related to this chapter. Type 1: Numerical on numbers
Q 1. The difference between two numbers is 1550. If 8 % of one number is 10 % of the other number, then find the two numbers
a. 4973, 6523
b. 5450, 7000
c. 6200, 7750
d. 6500, 4950
View solution Correct Option: (c)
Let two numbers be x and y.
It is given that, 8 % of x = 10 % of y
Therefore,
Difference between two numbers (x – y)= 1550
Substituting the value of x, we get
y=1550×4=6200
The two numbers whose difference is 1550 are 6200 and 7750. Q 2. Two numbers P and Q are such that, the sum of 2 % of P and Sum of 2 % of Q is twothird of the sum of 2 % of P and 6 % of Q. Find the ratio of P and Q.
a. 2 : 5
b. 3 : 1
c. 1 : 4
d. 5 : 1
View solution Correct Option: (b)
The sum of 2 % of P and Sum of 2% of Q is twothird of the sum of 2 % of P and 6 % of Q.
This sentence means that,
2% of P + 2% of Q =  2  (2% of P + 6% of Q) 
3 
2  P +  2  Q =  2   2  P +  6  Q  
100  100  3  100  100 
1  P +  1  Q =   1  P +  1  Q  
50  50  75  25 
Alternate method2  P +  2  Q =  2   2  P +  6  Q  
100  100  3  100  100 
Simply eliminate 100 from both the sides, we get
3(2P + 2Q) = 2(2P + 6Q)
6P + 6Q = 4P + 12Q
6P – 4P =12Q – 6Q
2P = 6Q
Q 3. 50 % of a number is 18 less than twothird of that number. Find the number.
a. 123
b. 119
c. 115
d. 108
View solution Correct Option: (d)
Let the number be x.
It is given that, 50 % of a number is 18, less than twothird of that number. This means that,
50x=5400
x=108
The number is 108 Q 4. When 35 is subtracted from a number; it reduces to its 80 %. Find the fourfifth of that number.
a. 140
b. 125
c. 137
d. 129
View solution Correct Option: (a)
We are given, 35 when subtracted from a number, reduces to its 80 %.
Therefore,
Let the number be x.
Solving, we get the value of x
Now, we are asked to find the fourfifth of that number i.e x
Hence, the number is 140.