How To Solve Percentage Questions Quickly

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?

Options:

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

1

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?

Options:

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?

Options:

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?

Options:

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?

Options:

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:

Options:

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