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Tips And Tricks And Shortcuts of Percentage
Tips ,Tricks and Shortcuts of Percentages
Percentage is the number expressed as a ratio multiplied by 100.. The symbol for the Percentage is “% ” .It is also written as “per cent” . which means for every 100.
Tips and tricks and shortcuts on Percentage
- Here, are quick and easy tips and tricks on PrepInsta page for Percentage problems swiftly, easily, and efficiently in competitive exams and other recruitment exams.
- If the value of an item goes up or down by x%, the percentage reduction or increment to be now made to bring it back to the original point is \mathbf{\frac{x}{100 + x } × 100 } %
- If A is x% more or less than B, then B is \mathbf{\frac{x}{100 + x } × 100 } % less or more than A.
- If the price of an item goes up/down by x %, then the quantity consumed should be reduced by \mathbf{\frac{x}{100 + x } × 100 } % so that the total expenditure remains the same.
- Percentage – Ratio Equivalence table
Fraction Percentage
| \frac{1}{3} × 100 = 33.33% | \frac{1}{10} × 100 = 10% |
| \frac{1}{4} × 100 = 25% | \frac{1}{11} × 100 = 9.09% |
| \frac{1}{5} × 100 = 20% | \frac{1}{12} × 100 = 8.33% |
| \frac{1}{6} × 100 = 16.66% | \frac{1}{13} × 100 = 7.69% |
| \frac{1}{7} × 100 = 14.28% | \frac{1}{14} × 100 = 7.14% |
| \frac{1}{8} × 100 = 12.5% | \frac{1}{15} × 100 = 6.66% |
| \frac{1}{9} × 100 = 11.11% | \frac{1}{16} × 100 = 6.25% |
Type 1: Percentage Tips and Tricks and Shortcuts- Based on Mixtures and Alligation
Question 1. A small container has 60l of milk and water mixture. It was made by mixing milk and water in which 80% is milk. Rohan came and added some water in the mixture. Now, find out how much water was added to the mixture that the percentage of milk became 60%?
Options:
A. 20 litre
B. 25 litre
C. 2 litre
D. 10 litre
Solution: Given, percentage of milk = 80%
It means, the percentage of water = 20%
In 60L of mixture, water = \frac{60 × 20 }{100} = \frac{1200 }{100} = 12 litre
Let the water added = x
Now, \frac{12 + x }{60 + x}× 100 = 40 (it is because in the new mixture milk is 60%, 100 – 60 = 40% water)
1200 + 100x = 2400 + 40x
100x – 40x = 2400 – 1200
60x = 1200
x= 20 litre
Correct option: A
Type 2: Percentage Tips and Tricks – Problems based on Ratios and Fractions
Question 1. If the numerator of a fraction is increased by 50% and the denominator is decreased by 10%, the value of the new fraction becomes \frac{4}{5} . Find the original fraction?
Options:
A. \frac{12}{21}
B. \frac{13}{20}
C. \frac{12}{25}
D. \frac{25}{12}
Solution: Let original numerator be x
Let original denominator be y
Let original fraction be \frac{x}{y}
According to the question,
Numerator of a fraction is increased by 50% = \frac{150}{100x}
Denominator is decreased by 10% = \frac{90}{100}
Now, \frac{\frac{150}{100} x }{ \frac{90}{100} y}= \frac{4}{5}
\frac{130x}{90y} =\frac{4}{5}
\frac{x}{y}= \frac{4}{5} × \frac{90}{150}= \frac{12}{25}
Correct option: C
Type 3: Tips and Tricks and Shortcuts for Percentages- Income, Salary, Expenditure
Question 1. Ajay spends 40% of his salary and saves Rs. 480 per month. Find his monthly salary.
Options:
A. 1000
B. 800
C. 600
D. 850
Solution: Let the salary of Ajay be x
He spends 40% which means he saves 60% of the salary.
60% of x = 480
\frac{60}{100}x = 480
x = 480 × \frac{100}{60}
x = \frac{48000}{60}
x = 800
Therefore, his monthly salary = 800
Correct option: B
Type 4: Percentage Tips and Tricks and Shortcuts- Problems based on Population
Question 1. Delhi has the population of 3000. In the first year, the population decreases by 4%, and in the second year, it increases by 5%. Find the population at the end of two years?
Options:
A. 3024
B. Remains same
C. 3120
D. 2880
Solution: In the first year, the population decreases by 4% = 3000 × \frac{96}{100} = 2880
In the second year it increases by 5% = 2880 × \frac{105}{100} = 3024
Correct option: A
Type 5: Problems based on profit and loss
Question 1. The cost price of 20 chairs is the same as the selling price of x tables. If the profit is 25%, then find the value of x?
Options:
A. 15
B. 20
C. 16
D. 18
Solution: Let the CP of each chair = 1
Therefore CP of x table = x
20 CP = X SP
Profit % = SP/CP
1.25=20/X
X=16
Correct option: C
Type 6: Percentage Tips and Tricks and Shortcuts
Question 1. If 20% of a = b, then b% of 20 is the same as:
Options:
A. 4% of a
B. 5% of a
C. 10% of a
D. 2% of a
Solution: 20% of a = b
\frac{20}{100} a = b
b% of 20 =\frac{b}{100} × 20
Now, \frac{20}{100}[/latex<strong>]</strong> a × \frac{b}{100} × 20
= 4% of a
Correct option: A
Read Also - How to solve Percentage Problems Quickly
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The cost price of 20 chairs is the same as the selling price of x tables. If the profit is 25%, then find the value of x? provided solution is not understandable kindly solve it again using some other methord