Percentage

Concept

Percentage is a method of expressing fractions or parts of a number or an object. The word ‘Percent’ means hundredth expressed by the symbol ‘%’. In another way percent is the portion of per hundred. For example, 10% of 50 = (10/50) x 100 = 100/5=20. Thus % is a number or ratio presented in the form of fraction of hundred.

Tips to solve problems on percentage:

The basic formula to find out percentage (%) = (Expectant Value/Total Value) x 100
Formula for Percentage (%) change = [(New Value-Original Value)/Original Value] x 100
In this formula-2, if (%) percentage change is positive, then it will be supposed that percentage (new value) increases and if it becomes negative, then it will be supposed that percentage (new value) decreases.

Q. If a company’s profits increased by 20% from 2021 to 2022 and then decreased by 10% from 2022 to 2023, what was the overall percentage change in profits from 2021 to 2023?

A) 20%

B) 12%

C) 8%

Profits increased by 20% from 2021 to 2022, which means that the new profit is 120% of the old profit. Then, profits decreased by 10% from 2022 to 2023, which means that the new profit is 90% of the old profit. Therefore, the overall percentage change in profits from 2021 to 2023 is: (120%)(90%) = 108%-100%=8%

D) 6%

Discuss

Q. Price of a product is increased by 20% and then due to mass protest the new price is again decreased by 20%. By how much the price increased or decreased in percentage?

A) -2%

B) -4%

Let, the original price $\displaystyle P = 100$ After a 20% increase, the price $\displaystyle P_{\text{new}} = P + (P \times 0.20) = 120$ Now, after a decrease by 20%, the new price $latex.php?latex=%5Cdisplaystyle+P %7B%5Ctext%7Bfinal%7D%7D+%3D+P %7B%5Ctext%7Bnew%7D%7D+$ So, the original price decreased by $\displaystyle \left(\frac{P - P_{\text{final}}}{P}\right) \times 100 = 4%$

C) 4%

D) 2%

Discuss

Q. Two numbers are less than a third number by 25% and 36% respectively. How much percent is the first number more than the second?

A) 21

B) 19

C) 12

D) 17

Answer: Let, the third number $\displaystyle = 100$ . Then the first number $\displaystyle = (100 - 25) = 75$ and the second number $\displaystyle = (100 - 36) = 64$ . So, the first number is more by $\displaystyle \frac{(75 - 64)}{64} = \frac{11}{64} \times 100 = 17%$

Discuss

Q. A man spends 80% of his income. If his income is increased by 30% as well as savings increased by 10%, his expenditure increased by what percentage?

A) 27%

B) 35%

Answer: Let, income be $\displaystyle I = 100$ , so savings $\displaystyle S = I - 80 = 20$ . After the increase, Income $\displaystyle I_{\text{new}} = I + (I \times 0.30) = 130$ and savings $\displaystyle S_{\text{new}} = S + (S \times 0.10) = 22$ . So, new savings $\displaystyle S_{\text{final}} = I_{\text{new}} - S_{\text{new}} = 108$ . Now, Expenditure increased $\displaystyle E_{\text{increase}} = S_{\text{final}} - 80 = 28$ . % of increase $\displaystyle = \left(\frac{E_{\text{increase}}}{80}\right) \times 100 = 35%$ .

C) 42%

D) 12%

Discuss

Q. If the price of onion is increased by 20%, find how much percent a man must decrease his consumption to keep the expenditure same?

A) 12%

B) 16.23%

C) 21%

D) 16.67%

Let, Price of onion $100 After increase, new price will be 100+(100+20)=$120 So, Consumption needs to decrease= $\displaystyle \frac{20}{120} \times 100=16.67%$

Discuss

Q. A number exceeds 21% of itself by 39.50. What will be the number?

A) 67

B) 55

Answer: $\displaystyle \frac{39.5}{100-21}\%$ = $\displaystyle \left(\frac{39.5 \times 100}{79}\right) = 50$

C) 42

D) 64

Discuss

Q. In a certain class 60% of the students are boys and rest are girls, among them 10% wear glasses. What percent of the students in the class are girls who wear glasses?

A) 8%

B) 6%

C) 4%

Let, the total number of students be $\displaystyle 100$ , where Boys are $\displaystyle (100 \times 60%) = 60$ & Girls are $\displaystyle (100 \times 40%) = 40$ . So, new girls who wear glasses $\displaystyle = 40 \times 10% = 4$ . Therefore, the percentage of Girls wearing glasses $\displaystyle = \left(\frac{4}{100}\right) \times 100 = 4%$ .

D) 5%

Discuss

Q. A marketing promotion officer receives monthly emolument of $20,000 and earns a commission of 20% on all product orders he receives. How much worth of order does he need to turn his monthly income of $30,000?

A) $30,000

B) $20,000

His monthly commission needed $(30,000-20,000)=$10000. This $10.000 is equal to 20% of order value he receives. Therefore, 100% of order value = $\displaystyle \left(\frac{10,000}{20}\right) \times 100 = 50,000$

C) $80,000

D) $60,000

Discuss

Q. In a shipment of individual products, 12% were defective and 50% of those defective repaired and restored by 15 lots. In another shipment of same products 10% were defective and 2% of those defective restored by 2 lots. For the two shipments combined, how many lots of products imported?

A) 1250

For shipment 1: Let, number of total lots $\displaystyle x$ , So, $\displaystyle (x \times 12%) \times 500% = x$ Or, $\displaystyle x = 250$ . For shipment 2: Let, Total number of lots $\displaystyle y$ . So, $\displaystyle (y \times 10%) \times 2% = 2$ Or, $\displaystyle y = 1000$ . Therefore, total lots imported $\displaystyle = 1000 + 250 = 1250$ .

B) 1680

C) 1030

D) 860

Discuss

Q. In a school cricket tournament a team won 10 matches out of 12 played where a match turned draw. It has 3 more matches to play. How many of matches must the team win to make a record of 80% win for the tournament?

A) 1

B) 4

C) 2

Let, ( x ) be the required number of tournaments. So, $\displaystyle \frac{(10+x)}{(12+3)} = 80%,$ Or, $\displaystyle 10+x = 12,$ Or, $\displaystyle x = 2.$

D) 6

Discuss

Q. In a class 20 students attended in final examination. Among them 29 students passed. The last student who passed, got 68% mark and thus secured 40 marks more than that of required to pass. The student who failed, got 50% mark and secured 50 marks less than required to pass. What was the percentage of marks required to pass?

A) 30

B) 50

C) 60

Answer: Let, ( X ) be the total marks. According to the question, $\displaystyle (68% \times X - 40) = (50% \times X + 50)$ , or, $\displaystyle 68% \times X - 50% \times X = 40 + 50$ , or, $\displaystyle 18% \times X = 90$ , or, $\displaystyle X = 500$ . So, pass marks $\displaystyle = (500 \times 50%) + 50 = 300$ . Percentage of marks to pass $\displaystyle = \left(\frac{300}{500}\right) \times 100 = 60%$ .

D) 35

Discuss

Q. In a college election between two candidates, the prime contestant secured 64% of the votes and was elected by a majority of 112 votes. What was the number of votes casted for opposition?

A) 196

B) 144

Answer: Winner got $\displaystyle 64%$ , so, opposition got $\displaystyle 100 - 64 = 36%$ . According to the question, $\displaystyle (64 - 36)% = 112$ , or, $\displaystyle 28% = 112$ . So, opposition got $\displaystyle \left(\frac{112}{28}\right) \times 36 = 144$ .

C) 180

D) 152

Discuss

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