What is the original fraction? - RACE 4 Bank · PDF...

1

Click here to load reader

Transcript of What is the original fraction? - RACE 4 Bank · PDF...

Page 1: What is the original fraction? - RACE 4 Bank  · PDF file¢Á¶¸-ÂÆjö¸:   EXPLANATIONS G.S. Giridhar Numerical Ability ANSWERS 1-C 2-E 3-D 4-B 5-B 6-D 7-A 8-D 9-C 10-B

í∫’®Ω’-¢√®Ωç 20 --W-Ø˛ 2013 Ñ-Ø√-úø’ £j«-ü¿®√-¶«-ü˛ 1

PERCENTAGE

PPercent is a fraction whose denominator ishundred.

The term percent means per every 100.40 percent means 40 out of 100.The Symbol % is used to denote percent.

Ex: 30%, 25%, 80% etc.★ Percent to Fraction: To convert percent

into fraction, divide the percent by 100.20 1

Ex: 20% = ⎯ = ⎯100 5

★ Fraction to Percent: To convert fractioninto percent, multiply the fraction by 100.

1 1Ex: − = − × 100 = 25%

4 4Increment

★ Increment % = ⎯⎯⎯⎯ × 100Source

15 −12Ex: Increment % in 12 and 15 is ⎯⎯ × 100

12= 25%

Decrement ★ Decrement % = ⎯⎯⎯⎯ × 100

Source

Ex: Decrement % in 12 and 15 is15 − 12⎯⎯⎯ × 100 = 20%

15

Ex: What is 37.5% of 1864?

Sol:3⎯8

× 1864 = 699

★ For converting one given quantity (x) as apercentage of another given quantity (y)

then x⎯y × 100.

Ex: 250 grams is what percent of 4 kilos?250

Sol: ⎯⎯ × 100 = 6.25%4000

(Both quantities are converted into same unit.)Note: Percentage is never expressed in any

units like litres or kilograms etc.★ When there are two articles 'a' and 'b' in a

group and in the ratio of a : b then to expressany one article as a percentage of thegroup, then

a∴ Percentage of 'a' = ⎯⎯ × 100

(a + b)b

And, Percentage of 'b' = ⎯⎯⎯ × 100(a + b)

Ex: In a library there are 550 English books225 Hindi books and 725 Telugu books.Find the percentage of Hindi books in thelibrary.

225Sol: ⎯⎯⎯⎯⎯⎯ × 100 = 15%

550 + 225 + 725★ When two variables are inversely propor-

tional, If one is x% More / Less than theother, then

xthe other is ⎯⎯⎯ × 100 Less / More

100 ± xNote: If first one is more use '+' and it is less

use ' − 'Ex: If the petrol rates are increased by 10%,

find by what percent a consumer has toreduce his consumption so that there is nochange in his expenditure on petrol.

10Sol: ⎯⎯ × 100 = 9

1⎯11

%110

Some more models

1. 32% of a number is 416. What is 43% ofthat number ?A) 416 B) 559 C) 403D) 384 E) None of these

Sol: 43⎯32

× 416 = 559

2. The sum of 55% of a number and 40% ofthe same number is 180.5. What is 80% ofthat number? (RBI Assts - 2012)A) 134 B) 152 C) 148D) 166 E) None of these

Sol: Sum of 55% and 40% = 95%If 95% value is 180.5

8080% value = ⎯ × 180.5 = 152

953. In an examination it is required to get 65%

of the aggregate marks to pass. A studentgets 825 marks and is declared failed by10% marks. What is the maximum aggre-gate marks a student can get?

(RBI Assts - 2012)A) 1450 B) 1640 C) 1500 D) Can't be determined E) None of these

Sol: 65% − 10% = 55%If 55% marks = 825, then

100100% (Total Marks) = ⎯ × 825 =1500

55

4. If the numerator of a fraction is increased by

20% and denominator is decreased by 10%,

the value of the fraction is 16⎯21

What is the original fraction?

A) 3⎯7

B) 5⎯11

C) 4⎯7

D) Can't be determined E) None of these

100 xSol: Let the fraction be ⎯⎯

100 y120x 16

∴ ⎯⎯ = ⎯90y 21

x 16 3 4⇒ ⎯ = ⎯ × ⎯ = ⎯

y 21 4 75. The price of an article was first increased by

10% and then decreased by 5%. What wasthe effective increase in the price of thearticle?A) 5% B) 5.5% C) 4.5% D) 15% E) None of these

Sol: For these type of questions xy

we can use x + y + ⎯⎯ formula100

(+10) × (−5)⇒ 10% − 5% + ⎯⎯⎯⎯⎯

100⇒ 10 − 5 − 0.5 = 4.5%

Some Important Percent Fractional Values

100% = 1 10% = 1⎯10

162⎯3

% = 1⎯6

50% = 1⎯2

20% = 1⎯5

331⎯3

% = 1⎯3

25% = 1⎯4

40% = 2⎯5

662⎯3

% = 2⎯3

12 1⎯2

% = 1⎯8

60% = 3⎯5

371⎯2

% = 3⎯8

61⎯4

% = 1⎯16

80% = 4⎯5

871⎯2

% = 7⎯8

75% = 3⎯4

125% = 5⎯4

EXERCISE

1. The length of a rec-tangle is increasedby 60%. By whatpercent would thewidth have to bedecreased to main-tain the samearea?A) 60% B) 55% C) 37.5%D) 40% E) None of these

2. If two numbers are respectively 20% and30% more then a third number, what per-centage is the first of the second?A) 10% B) 25% C) 12% D) 70% E) None

3. A person spent 85% of his monthly incomeand thereafter saves Rs.3600 per month.Find out his total income.A) Rs.12500 B) Rs.16200 C) Rs.26000 D) Rs.24000 E) None of these

4. In an examination it is required to get 441 ofthe aggregate marks to pass. A student gets

392 marks and is declared failed by5% marks. What are the maximumaggregate marks a student can get?A) 650 B) 980 C) 840D) Can't be determined E) None5. The difference between 63% of a

number and 45% of the same num-ber is 342. What is 78% of thatnumber?

A) 1342 B) 1482 C) 1558D) 1670 E) None of these

6. 48 percent of first number is 60 percent of

the second number. What is the respectiveratio of the first number to the second number?A) 4 : 5 B) 3 : 4 C) 4 : 7 D) 5 : 4 E) None

7. If the numerator of a fraction is increased by15% and denominator is decreased by 20%,

the value of the fraction is 23⎯60

. What is the

original fraction?

A) 4⎯15

B) 3⎯11

C) 7⎯15

D) Can't be determined E) None of these8. A student scores 20% marks and fails by 30

marks, while another student who scores32% marks, gets 42 marks more than theminimum required pass marks. What are themaximum marks for the examination?A) 800 B) 400 C) 500 D) 600 E) None

9. At an election conducted by two candidates,a candidate who gets 64% of votes wins bya majority of 252 votes. What is the totalnumber of votes?A) 800 B) 700 C) 900 D) 600 E) None

10. The difference between 42% of a numberand 28% of the same number is 210. Whatis 59% of that number?A) 670 B) 885 C) 460D) 900 E) None of these

[email protected] your suggestions and comments to

What is the original fraction?

2. Let the third number be 100, thenfirst number will be 120 and second numberwill be 130then percentage of First number to

120 4Second number is ⎯⎯ × 100 = 92 ⎯

130 133. If his monthly income is Rs.100

Saving = Rs.100 − 85 = Rs.15If saving is Rs.15 income is Rs.100∴ If saving is Rs.3600

100 × 3600income is = ⎯⎯⎯⎯ = Rs.24000

154. Marks required to pass is, 441− 392 = 49

Percentage marks required to pass = 5%∴ 5% = 49

100Total marks (100%) = ⎯⎯ × 49 = 980

55. Difference between 63% and 45% is 18%.

If 18% value is 342,78

78% value = ⎯ × 342 = 148218

6. Let the numbers be x and y48% x = 60% y

x 60= ⎯ = ⎯ ⇒ x : y = 5:4

y 48100 x

7. Let the fraction be ⎯⎯100 y

115x 23 x 23 16 4∴ ⎯ = ⎯ ⇒ ⎯ = ⎯ × ⎯ = ⎯

80y 60 y 60 23 15

8. 32% − 20% = 12%And 42 − (−30) = 72If 12% marks = 72

72 × 100Then 100% marks = ⎯⎯⎯ = 600

129. If winner gets 64%, the loser gets 36%

∴64% − 36% = 25228% of total votes = 252

100∴ Total votes (100%) = ⎯⎯ × 252 = 900

2810. 42 − 28 = 14% = 210

5959% value = ⎯⎯ × 210 = 885

14

à°‘ ô÷JïçÇçvüμ¿v°æü˨¸ ô÷Jïç úÁ´-©-°ˇ-¢Á’çö¸ 鬮Ìp-Í®-≠æØ˛

(à°‘-öÃ-úŒÆ‘) ¢Ë’ØË-ï®˝ §ÚÆæ’d© ¶μºKhéÀ (é¬çvö«èπ◊d v§ƒ-A-°æ-C-éπ†) ü¿®Ω-ë«-Ææ’h©’ éÓ®Ω’-ûÓçC.

ë«S©’: ¢Ë’ØË-ï®Ω’x – 10.Å®Ω|ûª: £æ«Ùô™¸ ¢Ë’ØË-ñ ¸-

¢Á’çö¸ / é¬uô-Jçí˚ õ„é¬o©@ /ô÷Jïç ¢Ë’ØË-ñ -̧¢Á’çö¸™ úÕvU/ áçHà ÖBh®Ω’g™„j Öçú≈L.Ææç•ç-Cμûª N¶μ«-í∫ç™ °æüË∞¡x ņ’¶μº´ç Å -́Ææ®Ωç.

´ßª’Ææ’: 45 à∞¡Ÿx N’çîª-èπÿ-úøü¿’.áç°œéπ: Éçô®Ω÷y u üΔy®√ü¿®Ωë«Ææ’h: ÇØ˛-™„j-Ø˛™ Ææ÷*ç-*† Nüμ¿çí¬

*´JûËC: V™„j 4¢Á¶ -̧ÂÆjö¸: www.aptdc.gov.in

áFd-°‘-Æ‘™ áTb-èπÿu-öÀ¢˛ võ„®·F©’ØË≠æ-†™¸ ü∑¿®Ωt™¸ °æ´®˝ 鬮Ìp-Í®-≠æØ˛ LN’-õ„ú˛

(áFd°‘Æ‘) áTb-èπÿu-öÀ¢˛ võ„®·F §ÚÆæ’d© ¶μºKhéÀ -ØÓ-öÀ°∂œÍé-≠æ-Ø˛ -N-úø’-ü¿-© -îËÆœç-C.

ë«S©’: áTb-èπÿu-öÀ¢˛võ„®·F (°∂jØ√Ø˛q) – 27

Å®Ω|ûª: Æ‘à / âÆ‘-úø•÷xuà ÖBh-®Ω’g™„j Öçú≈L.

´ßª’Ææ’: V™„j 8, 2013 Ø√öÀéÀ 29 à∞¡ŸxN’çîªèπÿúøü¿’.

áç°œéπ: ÇØ˛-™„jØ˛ áí¬b¢’̨, ví∫÷°ˇ úÕÆæ \-≠æØ˛, °æ®Ωq-†™¸Éçô®Ω÷y u üΔy®√. ü¿®Ω-ë«Ææ’h: ÇØ˛-™„jØ˛™

*´JûËC: V™„j 8¢Á¶ -̧ÂÆjö¸: www.ntpccareers.net

EXPLANATIONS

G.S. Giridhar

Numerical Ability

ANSWERS

1-C 2-E 3-D 4-B 5-B 6-D 7-A 8-D 9-C 10-B.

(Writer - Director, RACE Institute, Hyderabad)