Formulas and Quick Tricks for Percentage Problems
- a % of b = a * b/100
- If A is x% more than B, then B is less than A by: [x(100) / 100+x]%
- If A is x% less than B, then B is more than A by: [x(100) / 100-x]%
- If A is x% of C and B is y% of C, then A = x/y * B
- If the price of a commodity decreases by P %, then the increase in consumption so that the expenditure remains same, which is: [P(100) / 100-P]%
- If the price of a commodity increases by P%, then the reduction in consumption so that the expenditure remains same, which is: [P(100) / 100+P]%
- If a number is changed (increased/decreased) successively by x% and y%, then net% change is given by [x+y+(xy/100)]%, which
represents increase or decrease in value according as the sign is positive or negative
- If two parameters A and B are multiplied to get a product and if A is changed by x% and another parameter B is changed by y%,
then the net% change in the product (A * B) is given [x+y+(xy/100)]%
- In an examination, the minimum pass percentage is x%. If a student secures y marks and fails by z marks, then the maximum marks
in the examination is 100(y+z)/x
- If a number A is increased successively by x% followed by y% and then by z%, then the final value of A will be: A(100+x / 100) (100+y / 100) (100+z / 100)
Questions and Solved Examples on Percentage Problems
Q.1: For a candidate to clear an examination, he/she must score 55% marks. If he/she gets 120 and fails by 78 marks, the total marks for the examination is:
A. 300
B. 320
C. 360
D. 400
Answer: C. 360
Explanation: Here the mark obtained by the candidate is 120 and the candidate fails by 78 marks
Therefore the passing marks is (120+78) = 198
Let the total marks be x. Then,
=> 55/100 * x = 198
=> x = 360
Q.2: A property decreases in value every year at the rate of 6 1/4% of its value at the beginning of the year. It's value at the end of 3 years was Rs. 21,093. Find its value at the beginning of the 1st year?
A. Rs. 18,060.36
B. Rs. 18,600
C. Rs. 25,600.24
D. Rs. 32,000.50
Answer: C. Rs. 25,600.24
Explanation: 6 1/4% = 1/16
x * 15/16 * 15/16 * 15/16 = 21093
x = 25600.24
Percentage Problems – Basic Concepts, Formulas, Math Tricks, Quantitative Aptitude Questions and Solutions
Q.3: 80 is what percent of 64?
A. 75%
B. 85%
C. 120%
D. 125%
Answer: D. 125%
Explanation: Let x percent of 64 be 80
64 * x/100 = 80 => x = (80 * 100)/64 => x = 125
Hence, 80 is 125% of 64
Q.4: How much is 80% of 40 is greater than 4/5 of 25?
A. 4
B. 6
C. 9
D. 12
Answer: D. 12
Explanation: (80/100) * 40 – (4/5) * 25
32 – 20 = 12
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Q.5: 40% of a number is more than 20% of 650 by 190. Find the number?
A. 600
B. 700
C. 800
D. 900
Answer: C. 800
Explanation: (40/100) * X – (20/100) * 650 = 190
2/5 X = 320
X = 800
Q.6: 40 is subtracted from 60% of a number, the result is 50. Find the number?
A. 110
B. 130
C. 140
D. 150
Answer: D. 150
Explanation: (60/100) * X – 40 = 50
6X = 900
X = 150
Q.7: If A got 80 marks and B got 60 marks, then what percent of A's mark is B's mark?
A. 60%
B. 65%
C. 75%
D. 80%
Answer: C. 75%
Explanation: A's marks = 80; B's marks = 60.
Let x% of A = B => x/100 * 80 = 60
=> x = (60 * 100)/80 = 75
B's marks is 75% of A's marks
Q.8: A and B’s salaries together amount to Rs. 2,000. A spends 95% of his salary and B spends 85% of his. If now their savings are the same, what is A’s salary?
A. Rs.500
B. Rs.750
C. Rs.1250
D. Rs.1500
Answer: D. Rs.1500
Explanation: (5/100) A = (15/100) B
A = 3B, A + B = 2000
4B = 2000 => B = 500
A = 1500
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Q.9: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 3553, how much was it in the beginning?
A. 3800
B. 4200
C. 4400
D. 5500
Answer: C. 4400
Explanation: X * (95/100) * (85/100) = 3553
X = 4400
Q.10: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
A. 32%
B. 42%
C. 52%
D. 62%
Answer: C. 52%
Explanation: Total = 100, T = 40, NT = 60
40*(60/100) = 24, 60*(40/100) = 24
24 + 24 = 48 => 100 – 48 = 52%