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PERCENTAGEPercent means per every 100. 30 percent means 30 out of 100.

The symbol % is used to denote percent.

e.g.: 10%, 25% etc.

A fraction with denominator 100 is called per-centage.

Converting Percent to fraction:

To convert percent into fraction, divide thepercent by 100.

45 9e.g.: 45% = ⎯ = ⎯

100 20

Converting Fraction to percent: To convertfraction into percent, multiply the fraction by100.

3 3e.g.: ⎯ = ⎯ × 100 = 75%

4 4

IncrementIncrement percent = ⎯⎯ × 100

Source

DecrementDecrement percent = ⎯⎯ × 100

Source

e.g.: Ram's salary increased from Rs. 8000 toRs. 9000. Find the increment percent inhis salary.

A) 50% B) 25% C) 10% D) 12.5%

E) None of these

9000 - 8000Sol: Increment% = ⎯⎯ × 100

8000 1000⎯ × 100 = 12.5%. 8000

hence answer is (D)

e.g.: A man reduced the length of the tablefrom 5 m 60 cm to 4 m 80 cm. What is thepercentage decrement in the length of thetable?

A) 9.36% B) 14.28% C) 11.72%

D) 12.14% E) None of these

560 - 480Sol: Decrement% = ⎯ × 100

56080

= ⎯ × 100 = 14.28%, hence answer is (B).560

To express one given quantity (x) as a per-centage of another given quantity (y) we have

xto write ⎯ × 100.

y

e.g.: 720 millilitres is what percent of 6 litres?

720Sol: ⎯ × 100 = 12%

6000

Note: Percentage is never expressed in anyunit like litres, kilograms, rupees etc.

When there are three articles 'a', 'b' and 'c' ina group, then to express any one article as apercentage of the group, then

a∴ Percentage of 'a' = ⎯ × 100

(a + b + c)e.g.: A man has 5 red pens, 7 black pens and 8

green pens. Find the percentage of greenpens.

8Sol: ⎯ × 100 = 40%5 + 7 + 8

When two variables are inversely proportion-al, if one is 'x' percent more/less than the second

xone then the second one is ⎯ × 100

100 ± xpercent less/more than the first one.

Note: If first one is more use '+; and it is lessuse '-'.

e.g.: A's salary is 25% more than B's salary.Find by what percent B's salary is less thanA's salary.

A) 20% B) 75% C) 15% D) 25%

E) None of these

25Sol: ⎯ × 100 = 20%

100 + 25

(A's salary is more, + sign)

hence answer is (A)

e.g.: If the petrol rates are increased by 20%,find by what percent a consumer has toreduce his consumption so that there is nochange in his expenditure on petrol.

A) 20% B) 15% C) 12.5% D) 25%

E) None of these

20 2Sol: ⎯ × 100 = 16 ⎯ % hence answer is (E)120 3

If an objects value is increased/decreased by x% and other factorincreased/decreased by y%, then the net

xyeffects is [x + y + ⎯ ]%100

Note: The percentages are taken with posi-tive/negative sign according as there isincrease/decrease in the factor.

e.g.: In order to increase the total revenue, atrader announced 25% discount. As aresult, the sales volume increased by 20%.What is the net effect on the sales revenue?

A) 5% decrease B) 15% increase

C) 10% increase D) 20% decrease

E) None of these.

25 × 20 Sol:Neteffect is [-25 + 20 -⎯ ]% = -10%

100

10% decrease hence the answer is (E).

Some important Percents and their Fractions

1 2 1100% = 1 20% = ⎯ 16 ⎯ % = ⎯

5 3 6

1 2 1 150% = ⎯ 40% = ⎯ 33 ⎯ % = ⎯

2 5 3 3

1 3 2 225% = ⎯ 60% = ⎯ 66 ⎯% = ⎯

4 5 3 3

1 4 1 312.5% = ⎯ 80% = ⎯ 37 ⎯%= ⎯8 5 2 8

1 1 1 76.25% = ⎯ 10% = ⎯ 87⎯ % = ⎯

16 10 2 8

3 575% = ⎯ 125% = ⎯4 4

e.g.: What is 37.5% of 2168 ?

3Sol: ⎯ × 2168 = 819

8

Short cuts in calculating percents

e.g.: What is 15% of 3860?

Sol: 15% can be written as 10% + 5%

∴15% of 3860 = 10% + 5% of 3860⇒ 10% of 3860 = 386 and 5% of 3860

= 193 (half of 386)∴15% of 3860 = 386 + 193 = 579.

SOME MORE MODELS1. The difference between 82% of a number

and 27% of the same number is 385. What is43% of that number?

A) 385 B) 481 C) 528 D) 301

E) None of these

Sol: Difference between 82% and 27% is 55%

If 55% value is 385, then 43% value

43= ⎯ × 385 = 301

55 hence answer is (D)

2. A batsman scored 125 runs which included

12 boundaries and5 sixes. What per-cent of his totalscore did he makeby running betweenthe wickets?

A) 40% B) 35% C) 25% D) 12%

E) None of these

Sol: Runs made by running between the wickets

= 120 - (12 × 4 + 5 × 6)

= 120 - 78 = 4242∴ Required percentage = ⎯ × 100 = 35%120

hence, answer is (B)

3. In an examination it is required to get 328 of

the aggregate marks to pass. Astudent gets 287 marks and isdeclared failed by 5% marks.What are the maximum aggre-gate marks a student can get?

A) 369 B) 820 C) 615 D) 438 E) None of these

Sol: Marks required for thestudent to pass is, 328 - 287 = 41

Percentage marks required to pass = 5%

∴ 5% = 41100Total marks (100%) = ⎯ × 41 = 820,

5hence answer is (B)

4. Production of a company increases 8% peryear. If it is Rs. 225500 in 2007, what will beits production in 2009?

A) Rs. 3,25,750.00 B) Rs. 2,62,589.00 C) Rs. 2,63,023.20 D) Rs. 2,35,500.30 E) None of these

Sol: Production after two years (2009-2007)will be 108% of 108% of 225500

108 108⇒ ⎯ × ⎯ × 225500 = Rs. 263023.20100 100

hence, answer is (C)

45. A student multiplied a number by ⎯ instead of

33⎯ and got 427 more than the correct 4

answer. What is the original number?

A) 976 B) 549 C) 732 D) 854

E) None of these

Sol: Let the number be 'x'

4 3∴ ⎯ x - ⎯ x = 427 ⇒ x = 7323 4

hence the answer is (C)

6. Rajesh spends 12% of his monthly incomeon entertainment, 18% of his monthly incomeon children's education, 50% of his monthlyincome on other house-hold items and theremaining amount of Rs. 5200 he saves.What is his monthly income? (SBI 2009)

A) Rs. 25400 B) Rs. 26000

C) Rs. 24500 D) Rs. 27300

E) None of these

Sol: Total expenses percent

= 12% + 18% + 50% = 80%

Remaining percent = 100% - 80% = 20%

Saving money = Rs. 5200

∴ 20% = Rs. 5200100

Total money(100%) = ⎯ × 5200 = Rs. 2600020

hence answer is (B)

EXERCISE1. Find out 87.5% of Rs. 5920

A) 690 B) 4830 C) 2430 D) 5180

E) None of these

2. The length of the rectangle is doubled and

the breadth is halved. What is the percent-age change in the area?

A) 10% B) 15% C) 25%

D) No change E) None of these

3. A fruit seller sells 30% of apples and still has280 apples with him. Find the number ofapples he had originally.

A) 400 B) 1200 C) 600 D) 700

E) None of these

4. 45% of a number is less than its 64% by 38.What is 20% of that number? (SBI 2009)

A) 80 B) 40 C) 54 D) 190

E) None of these

5. A student score 24% marks and fails by 36marks while another student who scores32% marks, gets 12 marks more than theminimum required pass marks. What are themaximum marks for the examination?

A) 600 B) 1200 C) 800 D) 500

E) None of these

6. A man spends 14% of his monthly income onrent, 8% of his monthly income on schoolfees, 40% of his monthly income on clothes,19% of his monthly income oh house-holdexpenditure and saves remaining Rs. 5700.What is his yearly income?

A) Rs. 30,000 B) Rs. 2,60,000

C) Rs. 3,25,000 D) Rs. 3,60,000

E) None of these

7. 75% of a number is equal to three-seventh ofanother number. What is the ratio betweenthe first number and the second numberrespectively? (SBI 2009)

A) 3:4 B) 7:4 C) 4:7 D) 5:3

E) None of these

EXPLANATIONS7

1. ⎯ × 5920 = 51808

100 × 502. 100 - 50 - ⎯ = 0

100

∴ No change3. 30% sold means he has 70% with him

70% = 280

if 70% is 280, then 100% (total apples)

100 = ⎯ × 280 = 400

70

4. Difference between 64% and 45% is 19%

If 19% value is 38, then 20% value

20= ⎯ × 38 = 40

19

5. 32% - 24% = 8%

and 12-(-36) = 48; 8% marks = 48

100∴ 100% marks = ⎯ × 48 = 6008

6. Total expenses percent

= 14% + 8% + 40% + 19% = 81%

Remaining percent = 100% - 81% = 19%

Saving money = Rs. 5700

∴ 19% = Rs. 5700100

Total money (100%) = ⎯ × 5700 = Rs. 3000019

∴ yearly income is 30000 × 12 = Rs. 3,60,0003

7. Let the numbers be 'x' and 'y'. 75%x = ⎯ y7

3 3 x 3 4 4⇒ ⎯x = ⎯ y ⇒ ⎯ = ⎯ × ⎯ = ⎯

4 7 y 7 3 7∴ x : y = 4 : 7

What is his yearly income?What is his yearly income?Quantitative Aptitude

Key: 1) D 2) D 3) A 4) B 5) A 6) D 7) C

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