KKUNDAN

1. Two candidates contested the election. At the election 10%votes were rejected as invalid. The margin of the successfulcandidate was 308 and it was found that he had been sup-ported by 47% of the whole number on the voters list. Whatis the number of valid votes recorded by each candidate?

2. At a party 40% of the people have only orange juice andsnacks, 10% have only food and 80% have snacks. If no-body has all three and everybody has something, how manyhave at least food?

3. In a certain community consisting of p persons, x% canread and write. Among the males alone y% and of the fe-males alone m% can read and write. Find the number of malesand females in the community.

4. A man spends 80% of his income. With the increase in the

cost of living his expenses also increase by %2137 and his

income increases by %3216 . Find his present percentage

saving.

5. If the price of sugar falls by %212 a person can buy 9 kg

more of sugar for Rs 126 than before. If the price had risen by

%2112 , how much sugar could he have bought for the same

sum?6. In an examination paper of 5 questions, 5% of the candi-

dates answered all of them and 5% none. Of the rest, 25%answered only 1 question and 20% answered only 4. If

%2124 of the entire candidates answered only 2 questions

and 200 answered only 3, how many candidates appeared atthe examination?

7. A sum of Rs 2368 was divided among 8 men, 10 women and12 children in such a way that each man got 25% more thana woman and each woman got 25% more than a child. Howmuch did each woman get?

8. In a school 20% of the students are below 5 years of age and

the number of girls above 5 is 2

3of the number of boys above

5 and equal to 64. How many students are there in the school?

9. 662

3% of the employees of a company are skilled workers

and the rest are unskilled. If 40% of the skilled workers and

Percentage30% of the unskilled workers are temporary, find the totalnumber of employees when the toal number of permanentemployees is 456.

10. Entry fee in an exhibition was Re 1. Later this was reducedby 25%, which increased the sale by 20%. Find the percent-age increase in the number of visitors.

11. Total population of a country is 98 107, out of which 48 107 are females and the rest are males. Out of every 1000males 98 can read and write but only 7.5% of the total popu-lation can do so. Find what percentage of women in thewhole women population of the country can read and write.

12. In an examination paper of 6 questions, 5% of the candi-dates answered all the questions. Of the rest 10% answeredonly five questions out of six. Of the rest 20% answeredonly four questions out of six. Of the rest 25% answeredonly three questions out of six. Of the rest 3133 % answeredonly two questions out of six. Of the rest 50% answeredonly one question out of six. Of the rest 100% were unable tosolve any question out of the given six questions. Therewere 171 such students. Then what was the total number ofcandidates who appeared in the examination?

13. In a certain community consisting of P persons, a per centcan read and write. Of the males b percent and of the fe-males c percent can read and write. Find the number ofmales and females in the community.

14. In an examination paper of 6 questions, 4% of the candi-dates answered all of them and 6% none. Of the rest 20%answered only 1 question and 25% answered only 4. 15% ofthe entire candidates answered only 2 questions and 12%only 3 questions. If 220 candidates answered only 5, howmany candidates appeared at the examination?

15. The salaries of A, B and C together amount to Rs 25500. If

they spend 85%, 80% and %3278 of their respective sala-

ries, their savings are in the ratio 3 : 5 : 4. Find their respec-tive salaries.

16. There are two candidates in an election. 11% of the votersdid not vote. 500 votes were declared invalid. The electedcandidate got 3300 votes more than his opponent. If theelected candidate got 48% of the total votes, how manyvotes did each candidate get?

17. A man spends 75% of his income. With an increase in the

cost of living his expenditure increases by %3133 and his

income by 25%. Find his percentage of present saving.

KKUNDAN

1. Let x be the total voters.

No. of votes cast = 109x

Winner votes + Loser votes + 60 = 109x

Loser votes

= 100600043

1004760

109

xxx

According to the question,Winner Loser = 308

or, 308100600043

10047

xx

or, 3080060004347 xxor, 6200248004 xx Winner candidates valid votes

= 47% of 6200 = 2914 Loser candidates valid votes

2606100

6000620043

2.Juice Snacks (80)

40

0x y

10

FoodMaximum value of y = 80 40 = 40%Then maximum value of x = 100 (10 + 80) = 10% Maximum = 40 + 10 + 10 = 60% have food.

3. Let the number of males and females in the community be Aand B respectively.A + B = p ....(i)From the question,y% of A + m% of B = x% of por, xpmByA ....(ii)Multiply by y in equation (i), we get

ypyByA ....(iii)(ii) (iii)

yxpyByAmByA or, yxpymB

ymyxpB

Putting the value of B in equation (i), we get

ymyxppBpA

=

ymxmp

4. Let the income of man be Rs x.

Expenditure of man = 80% of x = Rs x54

saving =

54xx Rs 5

x

Answers and explanation

New income = 630050 xxxx = Rs x6

7

New expenditure = 20075

54

54

xx

= xxxxx

1011

1038

103

54

New saving = xx 1011

67

= Rs 15x

% saving = %755100

76

15

xx

5. %212 of 126200

5126 = Rs 2063

Reduced price of 9 kg of sugar = Rs 2063

Reduced price of 1 kg of sugar = 91

2063

= Re 207

Let the original price of sugar be Rs 100.

Reduced price = 212100 = Rs

2195

If reduced price is Rs 2

195, then original price

= Rs 100

If reduced price is Re 207

, then original price

= Re 2019572100

= Re 3914

Now, increased in the price = 2112100

= Rs 2

225

If original price is Rs 100, then increased price

= Rs 2

225

If original price is Re 3914

, then increased price

= 3914

1001

2225

= Re 5221

Sugar bought for Rs 126 = 2152126 = 312 kg

6. Let the total no. of candidates = xCandidate who answered 5 questions

= 5% of 20xx

Candidates who did not answer any question

KKUNDAN

= 5% of 20xx

Remaining candidates =

2020xxx

= xxx

109

10

Candidates who answered 1 question

= 25% of xx

409

109

Candidates who answered 4 questions

= 20% of xx

509

109

Candidates who answered 2 questions only

= %2124 of xx 200

49

Number of candidates who answered 3 questions

=

xxxxxx

20049

509

409

2020

= 4200150 xxx

Total no. of candidates = (x) = 4 200 = 8007. Suppose a child gets Rs x.

A woman gets = Rs

10025xx = Rs x

45

A man gets = Rs

xx

45 of %25

45

= Rs xxx 1625Rs

165

45

8 men get = Rs 81625

x = Rs x225

10 women get = Rs 1045 = Rs x

225

12 children get = Rs x 12 = Rs 12x

236812225

225

xxx

or, 37x = 2368 372368

x = Rs 64

Each woman gets = 6445 = Rs 80

8. Let the no, of students in the school = x no. of students below 5 years

= 20% of x = x/5No. of girls who are above 5 years = 64 no. of boys who are above 5 years

= 64 3/2 = 96

No. of students above 5 years = x - x5

45

x ..... (i)

No. of students in the school who are above5 years = 64 + 96 = 160 .... (ii)

From (i) and (ii),45

x = 160

x = 160 5

4

= 2009. Let the total no. of the employees in the company be x.

No. of skilled workers = 662

3% of x =

2

3x

unskilled workers = x - 2

3 3

x x

temporary workers = 40% of 2

3x + 30% of

x

3

= 4

15 10

8 3x

30

11

30x

x x

x

permanent workers = x - 11

30

19

30x x

From the question,19

30x = 456

x = 456 30

19

= 720

10. Let 100 persons visit the exhibition daily.Reduction in entry fee = 25% of Re 1 = Re 1/4

Reduced entry fee = 1 - 1

4 = Re

3

4Increase in sale of tickets due to reduction in entry fee = 20% total sale = 100 + 20% of 100 = Rs 120

If entry fee is Re 3

4, then no. of visitors = 1

If entry fee is Rs 120, then no. of visitors

=1 4 120

3

= 160

increase in daily no. of visitors= 160 100 = 60%

11. Total population = 980000000Number of males = 500000000Number of females = 480000000Number of persons who can read and write

= 735000001005.7980000000

No. of literate males

= 49000000100098500000000

No. of literate females = 73500000 - 49000000= 24500000

Percentage of literate females

= 48245

48000000010024500000 = 5.104%

12. Number of those students who answered zero question =171Suppose total number of students is T.

Then,

10025100

10020100

10010100

1005100T

100

50100100

3100100

= 171

KKUNDAN

or, 17110050

300200

10075

10080

10090

10095T

or, 100050200758090950003000000000171T

13. Let the number of males and females be M and F respec-tivelyThen M + F = PSince, of the males b per cent can read and write, then num-

ber of literate males = M100b

Similarly, number of literate females = F100c

But total number of literate people = P100a

P100aF100

cM100b

bM + cF = aPor, bM + c(P - M) = aPor, bM + cP - cM = aPor, M(b - c) = P(a - c)

or, cb

caPM

males

Also bM + cF = aPor, b(P - F) + cF = aPor, bP - bF + cF = aPor, F(c - b) = P(a - b)

or, F = bc

baP

females

14. Suppose total number of candidates = 100Candidates who answered 6 questions

= 4% of 100 = 4Candidates who didnt answer any question

= 6% of 100 = 6Remaining candidates = 100 - 10 = 90No. of candidates who answered only 1 question = 20% of90 = 18No. of candidates who answered only 4 questions = 25% of

90 = 2122

Candidates who answered only 2 questions= 15% of 100 = 15

Candidates who answered only 3 questions

= 2112 % of 100 = 2

112

No. of candidates who answered 5 questions

= 22211215

21221864100

If 5 questions are answered by 22 candidates then total no.of candidates =100

total no. of candidates = 100022022100

15. Let the salaries of A, B and C be Rs x, Rs y and Rs z respec-tively.Expenditure of A = 85% of x

Savings of A = 15% of x = Rs 20x3

Expenditure of B = 80% of ySavings of B = 20% of y = Rs y/5

Expenditure of C = %3278 of z

Savings of C = %3121 of z = Rs 75

z16

From the question,

75z16:5

y:20x3 = 3 : 5 : 4

x : y : z = 16475:55:3

203

= 20 : 25 : 475 = 80 : 100 : 75 = 16 : 20 : 15

Salary of A = 255005116 = Rs 8000

Salary of B = 255005120 = Rs 10000

Salary of C = 255005115 = Rs 7500

16. Let the total no. of votes = x% of voters who did not vote = 11%

no. of votes polled = 100x89

10011xx

Number of invalid votes = 500 no. of valid votes = (0.89x - 500) .... (i)Elected candidate gets 0.48x votes. Therefore0.48x + (0.48x 3300) = 0.89x 500or, 0.07x + 500 = 3300or, 0.07x = 2800or, x = 2800/0.07 = 40000 no. of votes secured by elected candidate

= 0.48x = 19200.No. of votes secured by loser candidate

= 19200 3300 = 1590017. Let his income be Rs 100.

expenses = 75% of 100 = Rs 75. savings = 100 75 = Rs 25.

Increased expenditure = 75 + 75 300100

= 75 + 25 = Rs 100.

Increased income = 125Rs10025100100

New savings = 125 100 = Rs 25.

% savings = %2010012525