How To Solve Percentage Questions Quickly

How to solve Percentages Problems Quickly

Here you will find easy tricks on How To Solve Percentage Problems quickly.

How To Solve Percentage Questions

Percentage Questions & Definition

  • A percentage is a ratio expressed as a fraction whose denominator (bottom) is 100.Thus, x percent means x hundredths, written as x%.
  • A percentage is a fraction of an amount expressed as a particular number of hundredths of that amount.

What is P percent of X?

  • Written as an equation: Y = P% × X.
  • The ‘what’ is Y that we want to solve for
  • Remember to first convert percentage to decimal, dividing by 100
  • Solution: Solve for Y using the percentage formula Y = P% × X.

How to calculate the percentage of a number?

  • To calculate the percentage of a number, we need to use a different formula such as:
  • P% of Number = X
    where X is the required percentage.
  • If we remove the % sign, then we need to express the above formulas as;
  • P/100 * Number = X

Type 1: Percentage Problems- based on Mixtures and Allegation

Question 1. A general store shopkeeper sells black pepper at some cost price but he mixes it with papaya’s seed and thereby gains 25%. Find the percentage of papaya’s seed mixed with black pepper?


A. 25%

B. 30%

C. 20%

D. 10%

Solution:     Let the CP of 1 kg black pepper = Re. 1

The SP of I Kg mixture = Re


Gain = 25%

Therefore, CP of 1 Kg

mixture = \frac{100}{125} × 1 = \frac{4}{5}

Ratio of black pepper: papaya seed = \frac{4}{5}: \frac{1}{5}

Hence, percentage of papaya seed in the mixture = \frac{1}{5} × 100 = 20%

Correct option: C

Question 2. A bar tender served a jar full of vodka containing 50% alcohol to a customer. After few minutes, the customer asked the bar tender to replace the vodka by another drink containing 19% alcohol and now the percentage of alcohol was found to be 25%. Find out the quantity of vodka replaced?


A. \frac{25}{31}

B. \frac{20}{31}

C. \frac{1}{2}

D. \frac{31}{20}

Solution:     By the rule of alligation, we have:

Ratio of 1st and 2nd quantities = 6: 25

By the rule of ratio, if x:y is the ratio, to get the quantity of x, the formula is \frac{x}{x+y},and to get the quantity of y, the formula is \frac{y}{x+y}

Therefore, required quantity replaced = \frac{25}{25 + 6} = \frac{25}{31}

Correct option: A

Question 3. There is one liquid A which contains 25% of water, the liquid B contains 30% of water. A vessel is filled with 6 parts of the liquid A and 4 parts of the liquid B. Find out the percentage of water in the mixture?


A. 27%

B. 25%

C. 20%

D. 30%

Solution:     Let the capacity of the vessel be 10

So, water from liquid A = 6 × \frac{25}{100} = 1.5

And, water from liquid B = 4 × \frac{30}{100} = 1.2

Total water = 1.5 + 1.2 = 2.7

In terms of percentage = \frac{2.7}{10} ×100 = 27%

Correct option: A

Type 2: Problems based on Ratios and Fractions

Question 1.If 40% of a number is equal to 2/3rd of another number, what is the ratio of first number to the second number?


A. 1: 2

B. 2: 3

C. 3: 5

D. 5: 3

Solution:     Let the two numbers be x and y

40% of x = \frac{2}{3}y

Then, \frac{40x}{100} = \frac{2}{3}y

  \frac{2}{5} x = \frac{2}{3}y

  \frac{x}{y} = \frac{2}{3} ×  \frac{5}{2} = \frac{5}{3}

Therefore the ratio = 5: 3

Correct option: D

Question 2: In a box of 8 donuts ,2 donuts have Choco chip sprinkle on them. Find out how many percent of the donuts in the box has Choco chip sprinkle?


A. 20%

B. 40%

C. 25%

D. 10%

Solution:     \frac{2}{8}= \frac{x}{100}

8x = 200

x = \frac{200}{8}

x = 25%

Correct option: C

Question 3: Two numbers are respectively 40% and 80% more than a third number. The ratio of the two numbers is:


A. 6: 5

B. 7: 9

C. 2:5

D. 1:2

Solution:     Let the third number x

First number = 40 % more than x = \frac{140}{100} x = \frac{7}{5} x

Second number = 80% more than x = \frac{180}{100} x = \frac{9}{5} x

Therefore their ratio = \frac{7}{5} x : \frac{9}{5} x = 7: 9

Correct option: B

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6 comments on “How To Solve Percentage Questions Quickly”

  • Hemant

    Question 3. Saloni’s salary was decreased by 30% and subsequently increased by 40%. How much percent does she loose?
    A. 16%
    B. 15%
    C. 12%
    D. 13%
    Solution: 100*(70/100)*(140/100) = 98
    So, 100-98=2
    %age = (2/100)*100 = 2%
    Is this right?

  • kaushal

    please help me m not able to follow the correct approach to follow the aptitude section all topics got mix up here