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# 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.

**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?**

**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**

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- Averages – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Allegations and Mixtures – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Ratio and Proportions – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Simple & Compound Interest – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Simple Interest – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Compound Interest – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts
- Profit & Loss – Questions | Formulas | How to Solve Quickly | Tricks & Shortcuts

**Others**

- Allegations and Mixtures – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Ratio and Proportions – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Simple & Compound Interest – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Simple Interest – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Averages – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Compound Interest – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Percentages – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts - Profit & Loss – Questions |

Formulas |

How to Solve Quickly |

Tricks & Shortcuts

**Others**

Question 3. Saloni’s salary was decreased by 30% and subsequently increased by 40%. How much percent does she loose?

Options:

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?

Its wright bro

in question 2 of type 5 option given is wrong but solution is right

We solve your issue. We hope you are doing great . All the best.

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Prepinsta Team

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

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