Percentage
Percentage
Important Formulas
 Concept of Percentage:By a certain percent, we mean that many hundredths.
Thus, x percent means x hundredths, written as x%.
To express x% as a fraction: We have, x% = x . 100
Thus, 20% = 20 = 1 . 100 5
To express a as a percent: We have, a = a x 100 %. b b b
Thus, 1 = 1 x 100 % = 25%. 4 4
 Percentage Increase/Decrease:If the price of a commodity increases by R%, then the reduction in consumption so as not to increase the expenditure is:
R x 100 % (100 + R)
If the price of a commodity decreases by R%, then the increase in consumption so as not to decrease the expenditure is:
R x 100 % (100 – R)
 Results on Population:Let the population of a town be P now and suppose it increases at the rate of R% per annum, then:
1. Population after n years = P 1 + R n 100
2. Population n years ago = P
1 + R n 100
 Results on Depreciation:Let the present value of a machine be P. Suppose it depreciates at the rate of R% per annum. Then:
1. Value of the machine after n years = P 1 – R n 100
2. Value of the machine n years ago = P
1 – R n 100
3. If A is R% more than B, then B is less than A by R x 100 %. (100 + R)
4. If A is R% less than B, then B is more than A by R x 100 %. (100 – R)
1
A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?  

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Answer: Option B
Explanation:
Number of runs made by running = 110 – (3 x 4 + 8 x 6)
= 110 – (60)
= 50.
Required percentage =  50  x 100  % = 45  5  %  
110  11 
2.
View Answer
Answer: Option C
Explanation:
Let their marks be (x + 9) and x.
Then, x + 9 =  56  (x + 9 + x) 
100 
25(x + 9) = 14(2x + 9)
3x = 99
x = 33
So, their marks are 42 and 33.
3.
A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:  

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Answer: Option D
Explanation:
Suppose originally he had x apples.
Then, (100 – 40)% of x = 420.
60  x x = 420  
100 
x =  420 x 100  = 700.  
60 
4.
What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?  

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nswer: Option C
Explanation:
Clearly, the numbers which have 1 or 9 in the unit’s digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69.
Number of such number =14
Required percentage =  14  x 100  % = 20%.  
70 
5.
If A = x% of y and B = y% of x, then which of the following is true?  

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Answer: Option E
Explanation:
x% of y =  x  x y  =  y  x x  = y% of x  
100  100 
A = B.
6.
If 20% of a = b, then b% of 20 is the same as:  

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Answer: Option A
Explanation:
20% of a = b  20  a = b. 
100 
b% of 20 =  b  x 20  =  20  a x  1  x 20  =  4  a = 4% of a.  
100  100  100  100 
7.
In a certain school, 20% of students are below 8 years of age. The number of students above 8 years of age is of the number of students of 8 years of age which is 48. What is the total number of students in the school?  

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Answer: Option E
Explanation:
Let the number of students be x. Then,
Number of students above 8 years of age = (100 – 20)% of x = 80% of x.
80% of x = 48 +  2  of 48 
3 
80  x = 80  
100 
x = 100.
8.
Two numbers A and B are such that the sum of 5% of A and 4% of B is twothird of the sum of 6% of A and 8% of B. Find the ratio of A : B.  

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Answer: Option D
Explanation:
5% of A + 4% of B =  2  (6% of A + 8% of B) 
3 
5  A +  4  B  =  2  6  A +  8  B  
100  100  3  100  100 
1  A +  1  B  =  1  A +  4  B  
20  25  25  75 
1  –  1  A =  4  –  1  B  
20  25  75  25 
1  A =  1  B  
100  75 
A  =  100  =  4  . 
B  75  3 
Required ratio = 4 : 3
9.
What is the percentage error in the calculation? 


View Answer
Answer: Option D
Explanation:
Let the number be x.
Then, error =  5  x –  3  x =  16  x. 
3  5  15 
Error% =  16x  x  3  x 100  % = 64%.  
15  5x 
10.
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:  

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Answer: Option A
Explanation:
Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
=  45  x 6000  = 2700.  
100 
11
Three candidates contested an election and received 1136, 7636 and 11628 votes respectively. What percentage of the total votes did the winning candidate get?  

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Answer: Option A
Explanation:
Total number of votes polled = (1136 + 7636 + 11628) = 20400.
Required percentage =  11628  x 100  % = 57%.  
20400 
12.
Two tailors X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?  

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Answer: Option B
Explanation:
Let the sum paid to Y per week be Rs. z.
Then, z + 120% of z = 550.
z +  120  z = 550 
100 
11  z = 550  
5 
z =  550 x 5  = 250.  
11 
13.
Gauri went to the stationers and bought things worth Rs. 25, out of which 30 paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?  

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Answer: Option C
Explanation:
Let the amount taxable purchases be Rs. x.
Then, 6% of x =  30 
100 
x =  30  x  100  = 5.  
100  6 
Cost of tax free items = Rs. [25 – (5 + 0.30)] = Rs. 19.70
14.
Rajeev buys good worth Rs. 6650. He gets a rebate of 6% on it. After getting the rebate, he pays sales tax @ 10%. Find the amount he will have to pay for the goods.  

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Answer: Option A
Explanation:
Rebate = 6% of Rs. 6650 = Rs.  6  x 6650  = Rs. 399.  
100 
Sales tax = 10% of Rs. (6650 – 399) = Rs.  10  x 6251  = Rs. 625.10  
100 
Final amount = Rs. (6251 + 625.10) = Rs. 6876.10
15.
The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:  

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Answer: Option B
Explanation:
Increase in 10 years = (262500 – 175000) = 87500.
Increase% =  87500  x 100  % = 50%.  
175000 
Required average =  50  % = 5%.  
10 