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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**

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