Here we provided formulae and hints for Percentage category. Requesting you to read the below points before taking online test.

Normally Percentage is defined as the fraction having denominator is 100 and numerator of the fraction is called rate of percent.

**Percentage is denoted by ‘%’ symbol.**

Tip-1

X % of Y ⇒ $ {X / 100} × Y $

**X % of Y = Y % of X**

Tip-2

If the new value of something is n times the previously given value, then the percentage increase is (n-1) × 100%

**Example**

**Question-1)**

** If X= 2.15 Y, then find the percentage increase when the value of something is from Y to X.**

** Solution:**

Use the formula: (n-1)×100% Percentage increase from Y to X = (2.15 -1)× 100= 115%

Tip-3

When a quantity N is increased by K %, then the:

New quantity = N $ (1+ K/100 )$

**Example**

**Question-2)**

**What is the new value when 265 is increased by 15%?**

**Solution:**

New quantity = N $(1+ K/100)$= 265$(1+15/100)$

New quantity = 1.15 ×265= 304.75

Tip-4

**When a quantity N is decreased by K %, then the: New quantity =N $(1 – K/100)$**

**Example**

**Question-3)**

If the production in 2022 is 3400 units and the decrease from 2020 to 2022 is 27%, find the production in 2020.

**Solution:**

New quantity = N $(1 – K/100)$= 3400$(1-27/100)$

New quantity = 3400 × 0.73= 2482

Tip-5

To calculate the percentage change in value

If the income of a man is A% more than another man, then the income of another man is less in comparison to the 1st man by

**Or, we can Say by Another Way**

If the cost of an product is increased by A%, then how much to decrease the consumption of product , so that expenditure remains same is given by

If 'x' is A% less than 'y', then y is more than 'x' by

**Or we can say by another way**

If the cost of an article is decreased by A%, then the increase in consumption of article to maintain the expenditure will be?

If value of an object/number/population P is successively changed by x%, y% and then z% in first, second and third year

Then, the **object/number/population** **changes after 3 years** = P$(1 ± {x}/100)(1 ± {y}/100)(1 ± {z}/100)$

**'+' **is used when **population increases**

**'–' **is used when **population decreases**.

**Both percentage changes are positive:**

x and y are positive and net increase = $(x+y+{xy}/{100})$ %.

**One percentage change is positive and the other is negative:**

x is positive and y is negative, then net percentage change = $(x-y-{xy}/{100})$%

**Both percentage changes are negative:**

x and y both are negative and imply a clear decrease= $(-x-y+{xy}/{100})$%

**Example**

**Question-4)**

**A’s salary is increased by 10% and then decreased by 10%. The change in salary is**

**Solution:**

Percentage change formula when x is positive and y is negative = $({x – y – ({xy}/{100})})$%

Here, x = 10, y = 10

= $(10 – 10 – {(10 × 10)}/{100}) $= -1%

As negative sign shows a decrease, hence the final salary is decreased by 1%.

Tip-9

**If an amount is increased by a% and then it is reduced by a% again, **

Then percentage change will be a decrease of **$a^2/100%$**

**Example**

**Question-5)**

The tax imposed on an article is decreased by 10% and its consumption increases by 10%. Find the percentage change in revenue from it.

**Solution:**

If an amount is increased by a% and then it is reduced by a% again, then the percentage change will be a decrease of $a^2/100$%

Required change = $(10)^2/100%$ decrease

= 1% decrease

Online Test - 1 (Percentage) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 2 (Percentage) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 3 (Percentage) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 4 (Percentage) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 5 (Percentage) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 6 (Percentage) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

Online Test - 7 (Percentage) TAKE TEST
Number of questions : 20 | Time : 30 minutes |

**Question-1)**

**89% of ? + 365 = 1075.22**

A) 798

B) 897

C) 898

D) 752

E) None of these

Ans: A

Solution: 89% of X = 1075.22 – 365 = 710.22

⇒$ {89 / 100} × X $ = 710.22

⇒X = ${710.22 × 100 } / 89$ = 798

**Question-2)**

**The difference between 78% of a number and 59% of the same number is 323. What is 62% of that number?**

A) 1054

B) 1178

C) 1037

D) 1159

E) None of these

Ans: A

Solution: According to given data,

⇒(78 – 59) % of X = 323

⇒ ${19 * X} / 100$ = 323

⇒ X = 1700

But we need to calculate 62% of 1700 = 1054

**Question-3)**

**Kiran spends 25% of his monthly income on household expenses. His annual income is Rs. 4.32 lac. What is the total amount that Kiran spends on household expenses in 8 months together?**

A) Rs. 74000

B) Rs. 71000

C) Rs. 73000

D) Rs. 72000

E) None of these

Ans: D

Solution: Annual Household expenses = $ {25% \text"of" \space 4.32 × 10^5}$

⇒$ 25 × 4.32 × 10^3$

Therefore household expenses for 8 months = $ {25 × 4.32} / {12 × 8 × 10^3} = 72000 $

**Question-4)**

**In an examination, it is required to get 296 marks out of aggregate marks to pass. A student gets 222 marks and is declared failed by 10% marks. What are maximum aggregate marks a student can get?**

A) 830

B) 810

C) 780

D) 740

E) None of these

Ans: D

Solution: Given data, assume maximum aggregate marks = P say

So, 10% of P = 296 – 222

⇒10% of P = 74

⇒P = 74 × 10 = 740