Tips and Tricks: Percentages | CSAT Preparation - UPSC PDF Download

Percentages

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
(Part/Whole)x100

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 
• 
• If A is x% more or less than B, then B isless or more than A.
  If the price of an item goes up/down by x %, then the quantity consumed should be reduced by less or more than A.
  If the price of an item goes up/down by x %, then the quantity consumed should be reduced by less or more than A.
  If the price of an item goes up/down by x %, then the quantity consumed should be reduced by so that the total expenditure remains the same.
• Percentage – Ratio Equivalence table

Fraction Percentage

Convert Percentages to Decimals or Fractions:

Sometimes it’s easier to work with decimals or fractions rather than percentages. To convert a percentage to a decimal, divide by 100. To convert a percentage to a fraction, simply write it over 100 and simplify if possible.

Practice Decimal Equivalents of Common Fractions:

Knowing common decimal equivalents of fractions (e.g., 1/4 = 0.25, 1/2 = 0.5, 3/4 = 0.75) can speed up your calculations.

Solving Percentage Increase/Decrease:

To find the percentage increase or decrease between two values, use the formula:

• Percentage Change = [(New Value – Old Value) / |Old Value|] * 100

Calculate Reverse Percentages:

If you have the final amount and the percentage increase/decrease and need to find the original amount, you can use this formula:

• Original Value = Final Value / (1 ± Percentage/100)

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 =
Let the water added = x
Now,  (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 4/5 . Find the original fraction?
Options:
A. 12/21
B. 13/20
C. 12/25
D. 25/12
Solution: Let original numerator be x
Let original denominator be y
Let original fraction be x/y
According to the question,
Numerator of a fraction is increased by 50% = 150/100
Denominator is decreased by 10% = 90/100
Now,


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

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 x 96/100 = 2880
In the second year it increases by 5% = 2880 x 105 x 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

= 4% of a
Correct option: A