Percentage

1. A mixture of 40 liters of milk and water contains 10% water. How much water should be added to this so that water may be 20% in the new mixture? 
Solution:
Mixture of 40 liters of milk=36M and 4W(Ratio is 90:10)
Now the New mixture shall be in the ratio of 80:20
Now water shall be added but milk shall not be touched
therefore 80% is equivalent to 36
100% is (36/80)*100=45
Thus water shall be added=(45-36-4)=5 liters of water

(or)

In a new mixture.. the milk should be 80%
so 36 ltr= 80%
so total will be 36*100/80= 45 ltr
hence added water is 45-40 = 5 ltr

2. The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:
Solution:
si of 4 month ie of 1/3 years=122
so p=2562-122=2440
now R=(si*100)/p*time

so R=122*100*3/2440*1=15

3. The price of petrol is increased by 10%. By how much percent the consumption be reduced so that the expenditure remains the same?
Solution:
9%
 using formulae [r/(100+r%)]*100

(or)

9% consumption has to be reduced.
because (91/100)*110 = 100

i.e 91 percent of (100 + 10) percent = 100 percent.

4. If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 8400 ?
Solution:
7*8400/200=294
10*8400/300=280

hence person has to pay 14 rs less as tax

5. Consider three brothers Ram, Ravi and Rahul. Consider Ram to be taller than Ravi by 10% and Rahul is taller than Ravi by 30%. Now, by how much percentage Rahul is taller than Ram.
Solution:
Let heights of Ram, Ravi and Rahul be p,q and r respectively. Then as per the conditions given in the question :

p = 110/100r and q = 130/100r
Ratios of heights of q and r will be (130/100r)/(110/100r) = 13/11.

Hence Rahul will be 13/11% taller than that of Ram.

6. Ravi had got twice as much as marks as Ramu. His teacher had made him a promise that, for every mark he scores above Ramu, he would be awarded 50% of those marks as bonus. Find the ratio of his bonus marks to the total marks of Ravi and Ramu.
Solution:
let ramu marks is 100 then ravi marks will be 200
bonus=200-100=100*50/100=50
then ratio: bonus/total marks

50/350=1:7

7. If the price of gold increases by 30%, find by how much the quantity of ornaments must be reduced so that the expenditure may remain the same as before?
Solution:
the formula for this situaion is..
100* (R)/(100+R)

100*30/130= 23.08 %

8. A student gets an aggregate of 60% marks in five subjects in the ratio 10 : 9 : 8 : 7 : 6. If the passing marks are 50% of the maximum marks and each subjects has the same maximum marks, in how many subjects did he pass the exam?
Solution
take the maximum mark in each sub as 100. qualify mark is 50.On a total dt fellow gets 60 x 5= 100.
We can write (10+9+8+7+6)a=300 => a=15/2
In 5 subjects he gets 75,67.5,60,52.5,45.

He passes in 4 subjects

9. The market value of a 10.5% stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being %, is:
Solution:
an income of rs 756 investment=rs 9000
for an income of rs 21/2 investiment is (9000/756*21/2)=125
for a rs 100 stoks,investment=rs 125
market value of rs 100 stocks=rs(125-1/4)
=rs 124.75

10. The banker's gain on a bill due 2 year hence at 10% per annum is Rs. 8. The true discount is:
Solution:
B.G=8
RATE=10
TIME=2
T.D=B.G*100/RATE*TIME
=8*100/2*10

=40

11. Find the number of ways in which 10 players out of 14 players can be selected such that 3 particular player are always included and 2 particular players are always excluded?
Solution:
Out of 14 players, let us element 2 particular player
which are excluded. Now, there are 12 players for selection of these 12, three have to be included in team always. Thus remaining players are (12 – 3) = 9 and the required players for team (10 – 3) = 7. Now,
selection cannot be done in
9C7 ways.

9C7 = 9!/7!2! = 36 ways.

12. When the price of a pair of shoes is decreased by 10%,the number of pairs sold increased by 20%.what is net effect on sales?
Solution:
Let the S.P be Rs 100 / shoe
Let 100 shoes are sold out
cost of shoe 10% decreased = ( 100- 10)= 90 Rs
20% Increase in sales therefore 120 shoes sold out
90*120=10800
100*100=10000
therefore (10800-10000)/100=800 

=> 8% increase in sales

13. The population of a village is 5500. If the number of males increases by 11 % and the number of females increases by 20 %, then the population becomes 6330. Find the population of females in the town?
Solution:
Let X is the initial population of Male and Y be the initial population of Female 
X + Y = 5500 .........(1)
If the number of males increases by 11 % and the number of females increases by 20 %, then 
Percentage problems for SSC RRB IGNOU Hotel Management exms
1.11 X + 1.2 Y = 6330 , On putting the value of X from equeation (1)
1.11 ( 5500 - Y ) + 1.2 Y = 6330
Y = 2500, 
Population of females in town

14. A shopkeeper sells milk which contains 5% water. What quantity of pure milk should be added to 2 liters of milk (containing 5% water) so that proportion of water becomes 4%?
Solution:
Present proportion of milk and water(in 2 litres of milk) is : 1900:100( in ml)
Now, let the milk should be added x ml
So, the new ratios is (1900+x):100
Hence, the equation becomes 100/(2000+x)=4/100
x comes to 500ml

Therefore, 500 ml of milk should be added so that the proportion of water becomes 4%


15. There are 600 tennis players 4% wear wrist band on one wrist Of the remaining, 25% wear wrist bands on both hands How many players don't wear a wrist band?
Solution:
here 4%=(4/100)*600 = 24
600-24=576
25%(576)=(25/100)*576 =144
no.of persons wear=144+24=168

no. of person not wearing wrist band
=600-168=432

16. In an examination of quantitative aptitude and logical reasoning. 65% examinees cleared quantitative aptitude test while 70% cleared logical reasoning test. If 50% examinees passed both the tests. then how many failed in both tests? 
Solution:
Total %age of student passed=65+(70-50)=85%

So,%age of student failed in both subject=15%

17. In a class the ratio of boys n girls is 5:6.if 25% of boys n 20% of girls r scholarship holders,find the %of students who r not scholarship holders?
Solution:
Let total students be x
No. of boys = 5/11*x
No. of girls = 6/11*x

Total no. of scholarship holders = 25/100*5/11*x + 20/100*6/11*x
=5/44*x + 6/55*x

Total no of students = No. of scholarship holders + No. of students who are not scholarship holders
x = 5/44*x + 6/55*x + No. of students who are not scholarship holders

No. of students who are not scholarship holders = 171/220*x=0.777x
% of students who are not scholarship holders = 0.777x/x*100

=77.7%

18. Shopkeeper rise price by 35% and gives successive discount of 10% and 15%. What is overall % gain or loss?
Solution:
Let d initial price be 100
35 % rise
now price = 135/100*100 = 135

10% discount 
Then price = 135 * 90/100 = 121.5

15 % discount
Then price = 121.5 * 85/100 = 103.275

So Gain = 103.275 - 100 = 3.275

Gain % = Gain * 100 /CP

==> 3.275 * 100 /100 = 3.275%


19. A and B invested Rs.4000 and Rs.5000 and they get 20% profit at the end of year. Then share of B is
Solution:
Total invest is 9000
20% gain of 9000 is 1800
A:B=4:5

B's share will be (5/9)*1800=1000

20. In a certain college, 20% of the boys and 40% of the girls attended the annual college outing. If 35% of all the students are boys, what percent of all the employees went to the outing?
Solution:
assume total students =100 in that 35 students are boys ,remaining 65 are girls........
20% of boys(35) =7
40% of girls(65) =26 
totally (26+7)=33 mems went to outing...... 33 is 33% in 100

so, the answer is 33%

21. Rani's weight is 25% of Meena's weight and 40% of Tara's weight. What percentage of Tara's weight is Meena's weight?
Solution:
Rani's weight=25% meera's weight = 40% tara's weight
meera's weight = 100/25*40% tara's weight

= 160% tara's weight

22. In a party , where there were 200 quests, 60% had veg food, 50% had non veg, 30% of guest had both veg and non veg, how many % did not dine at the party?
Solution:
Total guests =200
Dine members=(veg+nonveg - both)%
(60+50- 30)%
=80%
Not Dine members=100%- 80%
=20% of 200 

=40 members

23. A reduction of 20% in the price of sugar enables a consumer to obtain 2.5kg more for Rs.160. Find the reduced price per kg.of sugar.
Solution:
The extra 2.5 kg is obtained because of 20 reduction in price i.e. 20% of 160 = 32 rs.
Reduced price 1 kg = 32/2.5 = 12.80 rs.
So answer is 12.80 rs.
And original price :-
20% reduction price means you pay 80% of the original price
80% of original price = 12.80 rs/kg

100% of o.p. =16 rs/kg.

24. The total population of a village is 5000. The number of males and females increases by 10% and 15% respectively and consequently the population of the village becomes 5600. what was the number of males in the village ?
Solution:
let x be male, y be female

x + y = 5000 ---> (1)
x+10%x + y+15%y =5600
x + (10/100)x + y + (15/100)y=5600
(110/100)x + (115/100)y=5600
110x+115y=560000 --> (2)

solve (1) & (2)

110x+115y= 560000 --> (2)
-110x-110y=-550000 --> (1) * -110
-------------------
5y= 10000 
y= 2000
x+y =5000
y=2000 then x=3000 

No. of male in the village is 3000

25. In an examination, A got 10% marks less than B, B got 25% marks more than C and C got 20% less than D. If A got 360 marks out of 500. The percentage of marks obtained by D was :
Solution:
A got 369/500 * 100 = 72% 
This was 90% of B. So B = 72 * 100 / 90 = 80%. 

This was 125% of C. So C = 80 * 100 / 125 = 64%. 

This was 80% of D. So D = 64 * 100 / 80 = 80%. 
So D got 80% marks. 

26. The price of sugar is increased by 20%. As a result, a family decreases its consumption by 25%. The expenditure of the family on sugar will be decreased by :
Solution:
Let price of sugar be 100 and consumption be 100
original expenditure=price*quantity
=100*100
=10000
New expenditure=120*75
=9000
decrease in expenditure=[(10000-9000)/10000]*100

=10%

27. In an examination, 35% of the students passed and 455 failed. How many students appeared for the examination?
Solution:
if 35% of students passed then definitely 65% would have failed. rite!
let the total no of students be x.
so 65% of x=455 (i.e no of students failed)
65/100 x X = 455

SO X=455x(100/65)=700 students.

28. A's income is 25% more than B's income. B's income in terms of A's income is
Solution:
let us take b income=100
then A's income=125 
25 rs exceeding the B's
25/125*100=20

B's income is 80

(or)

[r/(100+r)] * 100 =80%


29. The price of oil is increased by 25%. If the expenditure is not allowed to increase, the ratio between the reduction in consumption and the original consumption is :
Solution:
Let the price be Rs 10 per litre and the consumption be 10 Kg
Given, increased price is 25% of 10 = 2.5 + 10 = Rs 12.5 per litre
So, according to the question if the price is not allowed to increase then how much can be consumed on the original price that is Rs 10
So, On 12.5 rupees the consumption is = 1 litre

On 1 rupee the consumption is = 1/12.5
On 10 rupees the consumption is = 1/12.5 X 10 = 4/5

So, for Rs 10 we consume only 4/5 litre instead of 1 litre
So, the reduction in consumption is 1 - 4/5 = 1/5
Therefore reduction in consumption : original consumption

That is, 1/5:1 = 1:5 

30. If the price of petrol increases by 25%, by how much must a user cut down his consumption so that his expenditure on petrol remains constant?
Solution:
let the petrol 1 unit initial price be rs 100.
25% increase on rs 100= rs 125
since expenditure to remain constant
125*x= 100*1
x=.80 unit

therefore consumer reduces =.20 unit i.e 20%

31. Fresh fruit contains 68% water and dry fruit contains 20% water.How much dry fruit can be obtained from 100 kg of fresh fruits ?
Solution:
The fruit content in both the fresh fruit and dry fruit is the same.
given,fresh fruit has 68% water.so remaining 32%(100-68) is fruit content.weight of fresh fruits is 100kg
dry fruit has 20% water.so remaining 80% is fruit content.let weight if dry fruit be y kg.
fruit % in freshfruit = fruit% in dryfruit
32/100 * 100 = 80/100 * y
we get y = 40 kg

32. If the price of sugar rises from Rs. 6 per kg to Rs. 7.50 per kg, a person, to have no increased in his expenditure on sugar, will have to reduce his consumption of sugar by 
Solution:
600/7.50=80%

so 20% reduced

33. The price of sugar increases by 32%. A family reduces its consumption so that the expenditure of the sugar is up by 10% only. If the total consumption of sugar before the price rise was 10 kg per month, then the consumption of sugar per month at present (in kg) is :
Solution:
let initially 10kg sugar= 100rs.
on increased price 10kg SUGAR= 132rs.
consumer uses sugar= 110rs.
therefore 1rs. sugar = 10/132kg

and 110rs. sugar = 10*110/132=8.3333

(or)

10kg-100rs
Now 10kg-132

so for 110rs u will get 1100/132=8.3333

34. Deven Invests Rs. 2,34,558 which is 25% of his annual income, in National Saving schemes. Whar is his monthly income?
Solution:
LET INCOME=X
25% OF X=234558
THEREFORE X=938232

monthly income= 938232/12=78186

35. In an examination, 80% of the students passed in English, 85% in Methematics and 75% in both English and Mathematics. If 40 students failed in both the subjects, the total number of students is :
Solution:
x*20%+x*15%-x*25%=40

x=Total Student=400

36. A reduction of 21% in the price of wheat enables a person to buy 10.5 kg more for Rs. 100. What is the reduced price per kg ?
Solution:
100 rs ------------xkg
79rs---------------x+10.5
21 rs----------10.5kg
x---------------1kg

x=21/10.5=2 

37. The present population of a country estimated to be 10 crores is expected to increase to 13.31 crores during the next three years. The uniform rate of growth is :
Solution:
population after n years = P(1+R/100)^n
13.31=10(1+R/100)^3
R=10% 

38. The population of a town increases 4% annually but is decreased by emigration annually to the extent of (1/2)%. What will be the increase percent in 3 years ?
Solution:
p(1+r/100)^n
r=3.5 
n=3
p=population 

ans 10.8

(or)

let initial population be 100.
after the end of year 1 population=100+3.5=103.5
after the end of year 2 population=103.5+103.5*3.5/100=107.12
after the end of year 3 population=107+107*3.5/100=110.8


so increase percentage =110.8-100=10.8


39. Ravi's salary was reduced by 25%.Percentage increase to be effected to bring the salary  to the original level is
Solution:
If initial salary is Rs 100.
After 25% reduction, salary will become Rs 75.
To make it again Rs 100, the salary should be increased by Rs 25.
So % increase required = 100*25/75= 100/3 % = 33 1/3 %

(or)

Taking 100 Rs as salary
Salary reduced by 25 % so salary is reduced 100 x 0.25 =25
So present salary is 100-25 = 75 Rs.
To take it Original value

75 Rs = 100 (I take 75 as 100%)
100 Rs =?

100 x 100
-----------
75
= 133.33 %
Difference

= 133.33-100 % = 33.33 % = 33 1/3% 

40. The boys and girls in a college are in the ratio 3 : 2. If 20% of the boys and 25% of the girls are adults, the percentage of students who are not adults is :
Solution:
let total students will be 100 divide it in 3:2 =60/40
20 % 60=12 boys adult
25 % 40= 10girls adults
total adults = 22
no of students =100

100-22=78

41. Water tax is increased by 20% but its consumption is decreased by 20%. Then, the increase or decrease in the expenditure of the money is 
Solution:
assume total amount is 100 
increased tax = 100+20 = 120
decrease in consumption = 100-20 =80
total amount 100*100 = 10000
after change 120*80 = 9600


(10000-9600/10000)*100 = 4 % decrease

42. A man’s income was reduced by 10%. How much percent it must now be raised so that it may be equal to the original amount?
Solution:
let income be 100
reduced by 10%
reduced income-90
diff required to cover original-10
10/90=11.111111111

So,answer is 11%

43. In an election contested by two parties, Party D secured12% of the total votes more than Party R. If party R got 132,000 votes, by how many votes did it lose the election?
Solution:
Let total % of votes secured by D = x 
Therefore, by R = ( x - 12)%
As there are only two parties, 
Thus, 
x + (x - 12) = 100
x = 56%
Therefore, R got (56 - 12) = 44%
By question, R got = 132,000
i.e; 44% (T) = 132,000
T = 3000,00 
Now, Party R lost by 12% (T)

= 36,000

44. In an election between two candidates, a candidate who gets 40% of total votes is defeated by 1500 votes. The number of votes polled by the winning candidate is :
Solution:
total votes be x
40% of x =60% of x - 1500
therefore,
20% of x=1500

i.e 60% of x =1500*3=4500

45. A cricket team won 40% of the total number of matches it played during a year. If it lost 50% of the matches played and 20 matches were drawn, the total number of matches played by the team during the year was :
Solution:
consider team played total x matches then,
40% of x+50% of x+20=x
90 5 of x+20=x
20=x-9x/10
20=x/10
x=200

so total matches played by team is 200

46. In a certain office, 72% of the workers prefer tea and 44% prefer coffee. If each of them prefers tea or coffee and 40 like both, the total number of workres in the office is :
Solution:
If the total no.of workers is 100 then 72 prefer tea and 44 prefer coffee.
n(Tea U Coffee) = n(Tea)+ n(Coffee) - n (Tea ^ Coffee)
100 = 72 + 44 - x (x: is workers who take both coffee and tea)
x = 116 - 100 = 16.
Therefore Out of 100 workers, 16 take both coffee and tea.
But as per the problem 40 take both coffee and tea

100 --- 16
? ----- 40

(40/16) * 100 = 250.

47. A student scores 55% marks in 8 papers of 100 marks each. He scores 15% of his total marks in English. How much does he score in English? 
Solution:
the total mark is (55/100)*800=440

15% of 440 is (440/100)*15=66

(or)

Given student scores 55% marks in english in 8 papers of 100 marks each.
so,his total marks are (55*800)/100 =>440
15% of his 440 marks is 440*(15/100)=>66

so,he scored 66 marks in english

48. There are 600 boys in a hostel. Each plays either hockey or football or both. If 75% play hockey and 45% play football, how many play both ?
Solution:
((75*600)/100)+((45*600)/100)-600
=120

(or)

450 members plays only hockey., 270plays only football. So both game players 120


49. Prices register an increase of 10% on food grains and 15% on other items of expenditure. If the ratio of an employee's expenditure on food grains and other items be 2 : 5, by how much should his salary be increased in order that he may maintain the same level of consumption as before, his present salary being Rs. 2590 ?
Solution:
Total expenditure= Rs. 2590
Let common ratio be x
then, expenditure on food grains=2x and expenditure on other items = 5x
therefore, 2x+5x=2590
7x=2590
x=370
so 2x = 2*370=Rs. 740 and 5x = 5*370=Rs. 1850
increase of 10% on food grains so new price= 740+10% of 740
 = 740+74=Rs. 814
increase of 15% on other items so new price= 1850+15% of 1850 
= 1850+277.5=Rs. 2127.50

Sum of increased prices=814+2127.50=Rs. 2941.50
difference between new expenditure and old expenditure
= 2941.50-2590=Rs. 351.50


50. In an examination, 35% candidates failed in one subject and 42% failed in another subject while 15% failed in both subjects. If 2500 candidates appeared at the examination, how many passed in either subject but not in both ? 
Solution:
both fail=15% only fail in sub1=20% and 
only fail in subject2
=(42-15)%=27%
so only pass in subject1=27% and only pass in subject2
= 20% so (20+27)%=47% 
passed in either subject but not both
now 100% =2500

so 47%=(2500/100) * 47
=1175

51. If the price of petrol increases by 25% and Kevin intends to spend only an additional 15% on petrol, by what percentage must he reduce the quantity of petrol purchased?
Solution:
Say cost of petrol is 100. 
New cost = 125. 
Now he spends only 115, so would get only 115/125 = 0.92 of the quantity. 

SO he should reduce his consumption by 8%

(or)

assume petrol price=100rs and he spends 100rs for petrol
25% increase --> 125rs
but he spends additional 15% only --> 115 rs

tat means reduce % = (115/125)*100 = 8%

52. Peter got 30%, of the maximum marks in an examination and failed by 10 marks. However, Paul who took the same examination got 40% of the total marks and got 15 marks more than the passing marks. What was the passing marks in the examination?
Solution:
let the max mark be x n passing mark be y.
peter got 30% of max mark =.3x i.e (x*30/100)
but he failed by 10 mark
therefore passing mark i.e y=.3x+10
now, paul got 40% of max mark=.4x
but he get 15 marks more than passing mark 
therefore passing mark i.e y= .4x-15

now from eq (i) n eq(ii)
.4x-15=.3x+10
x=250 i.e max mark
therefore passsing mark(put value of x)

y=.4x-15=.3x+10= 85

53. In an election between two candidates, one got 55% of total valid votes. 20% of the votes were invalid. If the total number of votes was 7500 the number of valid votes that the other candidate got was :
Solution:
total number of votes : 7500
invalid votes are : 7500*(20/100) =1500
then valid votes are : 7500-1500 = 6000
one member got : 6000*(55/100) = 3300

other candidate got : 6000-3300 = 2700

54. At an election involving two candidates, 68 votes were declared invalid. The wining candidate scores 52% and wins by 98 votes. The total number of votes polled is :
Solution:
let total valid votes be 100 winner gets 52 votes loser gets 48 votes difference 52-48=4 
so if difference is 4 then valid votes be 100 by this if difference is 98 then valid votes be 
(98/4)*100=2450 
total votes =2450+68(invalid votes)=2518

55. On increasing the price of T.V. sets by 30%, their sale decreases by 20%. What is the effect on the revenue receipts of the shop ?
Solution:
Let, price = Rs.100, sale = 100
Then, sale value = Rs.(100×100)=Rs.10000
New sale value = Rs.(130×80)=Rs.10400

INCREASE%=400/10000*1OO=4% increse

56.  5 litres of water is added to a certain quantity of pure milk costing $3 per litre. If, by selling the mixture at the same price as before a profit of 20% is made, what is the amount of pure milk in the mixture?
Solution:
3 rs/lit = 1.2 *[x (rs/lit)]

hence actual price = 2.5 rs /lit
hence 2.5/(3-2.5) = amount/5

amount = 25 lit

57. Salary of Suresh is 25% less than the salary of Ramesh. By how much percent the salary of Ramesh is more than the salary of Suresh?
Solution:
using (r/100-r)100%
=25/75*100

=33 1/3%

58. The value of a machine depreciation at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :
Solution:
let x be the initial price.....
a/c question x*(1-(1/10))^3=8748

i-e:x=8748*(1000/729)=12000

59. At an election a candidate who gets 84% of the votes is elected by a majority of 476.Votes what is the total number of votes polled?
Solution:
84x-16x=476
68x=476

x=700

60. 5% of (25% of Rs1600) is
Solution:
25% of 1600=(25*1600)/100=400

5% of 400=(5*400)/100=20

61. If the cost of rice decreases by 20%, a man is able to buy 25 kg more for Rs.1000. Find the Cost Price per kg
Solution:
let earlier cost was Rs 100. 20% dec means Rs 80
let earlier he could bought x kg and now x+25
so x*1000=80*(x+25)
x=100
so 1000/100=10 Rs
now 1000/125=Rs 8

so price per kg is rs 8 

62. The price of sugar increases by 20%. By what percent must a house wife reduce the consumption of sugar, so that the expenditure on sugar is the same as before ?
Solution:
20/120*100=16.67

63. Raman's salary was decreased by 50% and susequently increased by 50%. He has a loss of :
Solution:
first take salary is 100%
100-50/100*100 = 50%
50+50/100*50 = 75%
so 100-75=25%

so decrease is 25%

64. 30% of the men are more than 25 years old and 80% of the men are less than or equal to 50 years old. 20% of all men play football. If 20% of the men above the age of 50 play football, what percentage of the football players are less than or equal to 50 years?
Solution:
20% of the men are above the age of 50 years. 20% of these men play football. Therefore, 20% of 20% or 4% of the total men are football players above the age of 50 years. 

20% of the men are football players. Therefore, 16% of the men are football players below the age of 50 years.


Therefore, the % of men who are football players and below the age of 50=(16/20)×100= 80%


65. 5000 votes in an election, 14% invalid. The Winner won by a margin of 15%. Find the number of votes secured by the winner
Solution:
14% are invalid...so 5000*14/100 =4300.
if we consider no of votes secured by winner is y, then the other candidate secures 4300-y votes. given difference between them is 15 % of the valid votes.
hence, y-(4300-y)=15*4300/100....

y=2472.5...approximately 2473

66. if there are 5,000 voters out of which 20% are not eligible to vote and there are two candidates contesting? The winning candidates won by 15% of votes? what is the total number of votes he got ?
Solution:
5000*.8=4000
4000*.15=600
x-(4000-x)=600

x=2300

67. A candidate who gets 20%marks fails by 11 marks but another candidate who gets 42% marks gets 22 marks more than the passing marks. Find the maximum marks.
Solution:
x*20/100+11=x*42/100-22

solve this question x=150

68. 75% of the participants in a graduation ceremony will receive an honorary award If 400 people participated in the ceremony, how many more people will receive awards than those who will not?
Solution:
25%400=100
75%400=300

300-100=200.

69. The Maruti price has risen by 25% and the sales have come down by 4%. What is the total percentage change in revenue?
Solution:
let initial price=100 n sales=100
initial revenue=100*100=10000
final price=125 n sales=96
final revenue=125*96=12000

%age change=(12000-10000/10000)*100=20

70. A man spends 75% of his income. His income increases by 20% and he increased his expenditure by 15%. His saving are then increased by 
Solution:
Let income = Rs. 100 
.-. Expenditure = Rs. 75 Saving = Rs. 25
New income = Rs. 120 
.-. Expenditure = (115/100) X 75 = 345/4
Saving = 120 - (345/4) = 135/4

Increase % in saving = (35/4) X (1/25) X 100 = 35%

71. Mukesh has twice as much money as Sohan and Sohan has 50% more money than what Pankaj has. If the average money with them is Rs. 110, then Mukesh has
Solution:
Let Mukesh ,Sohan and m,s,p resp.
then m=2s ,s=p*3/2
then avg =(2s+s+2/3*s)/3=110
so,s=90

m=2*s=2*90=180.

72. 1100 boys and 700 girls are examined in a test; 42% of the boys and 30% of thegirlsPass.The percentage of the total who failed is:
Solution:
Number of boys passed in the exam=(1100*42)/100=462
Boys failed in the exam=1100-462=638
Number of girls passed in the exam=(700*30)/100=210
Girls failed in the exam are=700-210=490

Total number of students failed in the exam=638+490=1128

Percentage of students who failed in exam 
=(1128*100)/1800=62.66

73. Anil's height is 20% less than Deepak's. How much is Deepak's height more than Anil's ?
Soluton:
{100*20/(100-20)}%=25%

74. If the price of petrol increases by 25 and kevin intends to spend only 15% more on petrol.By how much percent should he reduces the quantity of petrol that he buys?
Solution:
Let C.P = 100
petrol increased by 25 = 125 (new C.P)
Kevin spend only 15% = 115
(115/125)*100 = 92 ltr

100-92 = 8 %

75. Mr.John used to purchase certain number of mangoes for $360. Since the price of mangoes is reduced by 10% he got 12 more mangoes today. Find the original price of 120 mangoes
Solution:
let cost of mangoes be 'm'
10% of 360 = 12m
(10/100) * 360 = 12m
36 = 12m
m=3

cost of 120 mangoes = 120*3 
= $360

76. The retail price of rice decreased from Rs. 16 kg to Rs. 12 per kg. Find the percentage decrease. 
Solution:
decrease:16-12=4
%decrease=4/16*100

ans:25

77. The monthly salary of Mr. Anand is Rs. 8500. He spends 20% on education of his children, 25% as house rent, 30% on food, 5% on travels, 8% on miscellaneous things and rest he saves. Find his annual savings. 
Solution:
his total spendings are :20+25+30+5+8=88%
so total savings=12% of 8500 =1020

but anually he saves =12*1020 =12240