# percentage problems and solutions

**percentage problems and solutions**

**Question1**: Ravin spends 10% of his pocket money to buy chocolates and 20% to buy books and saved the rest. If he got Rs.1200 as his pocket money, how much did he save?

Option 1 : Rs.480

Option 2 : Rs.360

Option 3 : Rs.840

Option 4 : Rs.720

Answer : C

**Explanation**: He saved 70% of his pocket money.

70% of 1200

= (70/100)*1200

= 840

**Question2**: If the area of a square is increased by 69%, by how much % does the side of the square increase?

Option 1 : 30%

Option 2 : 34.5%

Option 3 : 8.3%

Option 4 : 13%

Answer : A

**Explanation**: Let the area of the original square be a² sq.units

Area of the new square

= 1.69a²

Side of the square

= √(1.69a²)

= 1.3 a

Sides increase by 30%

**Question3**: 52% of the people in a village are male and 48% female. If 55% of the males and 45% of the females are educated, find the percentage of educated people in the village.

Option 1 : 50.2%

Option 2 : 50%

Option 3 : 49%

Option 4 : 49.8%

Answer : A

**Explanation**: Let the population be x.

% of educated people

= [55% of 52% of x]+[45% of 48% of x]

= [28.6% of x]+[21.6% of x]

= 50.2% of x

50.2% of the people are educated.

**Question4**: Successive discounts of 15%, 10% and 10% on a product is equal to a single discount of

Option 1 : 35%

Option 2 : 31.15%

Option 3 : 30%

Option 4 : 28.85%

Answer : B

**Explanation**: Price of the product after discount

= (85/100)*(90/100)*(90/100)*SP

= 0.6885 SP

Discount %

= (1-0.6885)*100

= 31.15%

**Question5**: An agent gets 2% of the selling price as his commission for every property he sells. If he helped a seller sell a property for Rs.30,00,000, find his commission.

Option 1 : Rs.6,00,000

Option 2 : Rs.60,000

Option 3 : Rs.1,50,000

Option 4 : Rs.15,000

Answer : B

**Explanation**: Commission

= 2% of 30,00,000

= 60,000

**Question6**: A fruit vendor sells 80% of the oranges he had and discards 25% of the remainder. Next day, he sells 80% of the remainder and discards the rest. What % of the oranges does he discard?

Option 1 : 8%

Option 2 : 4.5%

Option 3 : 5%

Option 4 : 20%

Answer : A

**Explanation**: Let the number of oranges he had in the beginning be x.

Day 1:

He sold 80% = 0.8x and has 0.2x left.

Discarded 25% of the remaining 0.2x

No. of oranges discarded

= 25%*0.2x

= 0.05x

No. of oranges left

= 0.2x-0.05x

= 0.15x

Day 2:

Sold 80% of 0.15x

= 0.12x

Discarded the rest

= 0.15x-0.12x

= 0.03x

Total oranges discarded

= 0.05x+0.03x

= 0.08x

= 8% of x

**Question7**: Vimal scored 93% in his exams. If he scored 84 marks less than the maximum marks, find the maximum marks.

Option 1 : 500

Option 2 : 1200

Option 3 : 1100

Option 4 : 700

Answer : B

**Explanation**: He scored 7% less than the maximum marks.

7% of x = 84

x = 1200

**Question8**: What % of 10 is 10% of 1?

Option 1 : 10

Option 2 : 0.01

Option 3 : 0.1

Option 4 : 1

Answer : D

**Explanation**: (x/100)*10 = (10/100)*1

x = 1

x% of y = y% of x

**Question9**: In an election, the winning candidate got 58% of the valid votes. If he got 1600 votes more than the other candidate and 100 votes were invalid, find the number of votes cast.

Option 1 : 12500

Option 2 : 16100

Option 3 : 10100

Option 4 : 15600

Answer : C

**Explanation**: Let the no. of valid votes be x

Winning candidate - 58% of x

Other candidate - 42% of x

Difference - 16% of x

16% of x = 1600

x=10000

Total votes

= 10000+100

= 10100

**Question10**: A two digit number ab is 60% of x. The two-digit number formed by reversing the digits of ab is 60% more than x. Find x.

Option 1 : 72

Option 2 : 36

Option 3 : 90

Option 4 : 45

Answer : D

**Explanation**: Let the digits of the number be a and b.

10a + b = 0.6x

10b + a = 1.6x

Subtracting one from the other, we get

9b - 9a = x or x = 9( b-a)

x should be a multiple of 9.

0.6 = 3/5

10a + b = 3x/5, this implies that x should also be a multiple of 5.

Or, x should be a multiple of 45

x should be equal to 45, ab = 27, ba = 72

**Question11**: The population of a town was 1,00,000 three years ago. If it increased by 2%, 3% and 5% respectively in the last three years, then the present population of the town is

Option 1 : 1,10,562

Option 2 : 1,10,000

Option 3 : 1,10,313

Option 4 : 1,11,237

Answer : C

**Explanation**: The present population

= (102/100)*(103/100)*(105/100)*100000

= 1,10,313

**Question12**: Out of the first 75 natural numbers, what percentage of them have 7 either in the units place or in the tens place?

Option 1 : 18.67%

Option 2 : 17.33%

Option 3 : 16%

Option 4 : 17%

Answer : B

**Explanation**: There are 13 numbers.

(7, 17, 27, 37, 47, 57, 67, 70, 71, 72, 73, 74, 75)

(13/75)*100 = 17.33%

**Question13**: 40% of a number is 80. What is 30% of one-fourth of the number?

Option 1 : 60

Option 2 : 15

Option 3 : 9.6

Option 4 : 30

Answer : B

**Explanation**: (40/100)*x = 80

x = 200

(30/100)*(200/4) = 15

**Question14**: After selling 35% of the oranges, a fruit vendor has 260 oranges left. How many did he have originally?

Option 1 : 400

Option 2 : 520

Option 3 : 390

Option 4 : 300

Answer : A

**Explanation**: After selling 35% of the oranges, he has 65% left.

(65/100)*x = 260

x = 400

**Question15**: If x=3y, what % of x is y?

Option 1 : 3%

Option 2 : 10%

Option 3 : 30%

Option 4 : 33.33%

Answer : D

Explanation : y = x/3 = (1/3)*x

= (100/3)% of x

= 33.33% of x

= (100/3)% of x

= 33.33% of x

**Question16**: In a cricket match, Rahul scored a century with 13 boundaries and 3 sixes. What percentage of his runs did he make by running between the wickets?

Option 1 : 70%

Option 2 : 50%

Option 3 : 35%

Option 4 : 30%

Answer : D

**Explanation**: Runs scored in boundaries and sixes

= (13*4)+(3*6)

= 52+18 = 70

Runs scored between the wickets

= 100-70 = 30

30% of the runs are scored by running between the wickets.

**Question17**: In a class, there are 50 students. A teacher selects 10 students for a competition. The number of boys selected is 32% of the total number of boys and the number of girls selected is 8% of the total number of girls in the class. Find the number of girls in the class.

Option 1 : 20

Option 2 : 24

Option 3 : 25

Option 4 : 30

Answer : C

**Explanation**: Let the no. of boys and girls in the class be x and y respectively.

x+y=50

0.32x+0.08y=10

Solving the two equations, y=25

**Question18**: Rahul scored 75 marks in the first internal and 90 marks in the second internal. By how much percentage has Rahul’s performance improved?

Option 1 : 15%

Option 2 : 20%

Option 3 : 25%

Option 4 : 30%

Answer : B

Explanation : % improvement

= [(90-75)/75]*100

= 20%

= [(90-75)/75]*100

= 20%

**Question19**: A group of 300 consists of 135 senior citizens. If 40% of the women in the group are senior citizens and there are 200 men in the group, find the number of male senior citizens in the group.

Option 1 : 95

Option 2 : 40

Option 3 : 45

Option 4 : 120

Answer : A

**Explanation**: Let a and b be the number of Male Senior Citizens and Male Non-Senior Citizens respectively.

Let c and d be the number of Female Senior Citizens and Female Non-Senior Citizens respectively.

a+b=200

a+c=135

a+b+c+d=300

0.4*(c+d)=c

Solving the four equations, a=95

**Question20**: A group consists of 60% men and 40% women. 70% of the people in this group are employed. If 100 men are employed and 50% of the women are employed, find the number of people in the group.

Option 1 : 150

Option 2 : 175

Option 3 : 200

Option 4 : 250

Answer : C

**Explanation**: Let the number of people in the group be x.

Number of men = 0.6x

Number of women = 0.4x

Number of employed = 0.7x

100+0.5*(0.4x) = 0.7x

x=200

**Question21**: The sides of a cube are increased by 10%. By how much will the volume of the cube increase?

Option 1 : 22%

Option 2 : 30%

Option 3 : 33.1%

Option 4 : 35%

Answer : C

**Explanation**: New volume

= (1.1a)³ = 1.331a³

% increase = 33.1%

**Question22**: If the length and area of a rectangle have been increased by 20% and 32% respectively, by how much % has the breadth been increased?

Option 1 : 15%

Option 2 : 12%

Option 3 : 11%

Option 4 : 10%

Answer : D

**Explanation**: New breadth

=1.32lb/1.2l = 1.1b

% increase in breadth = 10%

**Question23**: If the length and breadth of a rectangle is increased by 15% and 20%, by how much will the area of the rectangle increase?

Option 1 : 38%

Option 2 : 35%

Option 3 : 32%

Option 4 : 30%

Answer : A

**Explanation**: Area of the new rectangle

= 1.15l*1.2b

= 1.38lb

% increase in area = 38%

**Question24**: If the sides of a square are increased by 20%, by how much will the area of the square increase?

Option 1 : 40%

Option 2 : 20%

Option 3 : 50%

Option 4 : 44%

Answer : D

**Explanation**: Area of the original square

=a²

Area of the new square

= (1.2a)²=1.44a²

% Increase in area

= [(1.44a²-a²)/a²] * 100

= 44%

**Question25**: If the length and breadth of a cuboid are halved and the height is doubled, find the % change in volume.

Option 1 : 50% increase

Option 2 : 25% increase

Option 3 : 50% decrease

Option 4 : 25% decrease

Answer : C

**Explanation**: New volume

= (l/2)*(b/2)*2h

= (lbh/2)

So, there is 50% decrease.

**Question26**: If the sides of a square are decreased by 10%, by how much does the area of the square decrease?

Option 1 : 20%

Option 2 : 19%

Option 3 : 15%

Option 4 : 10%

Answer : B

**Explanation**: Side of the new square

= 0.9a

Area of the new square

= (0.9a)² = 0.81a²

19% decrease

**Question27**: Daal is now being sold at Rs. 20 a kg. Last month, its rate was Rs. 16 per kg. By how much percent should a family reduce its consumption so as to keep the expenditure fixed?

Option 1 : 25%

Option 2 : 20%

Option 3 : 5%

Option 4 : 4%

Answer : B

**Explanation**: Let a family’s monthly consumption of daal be x kg.

To keep the expenditure fixed, their consumption for this month should be 16x/20 = 4x/5.

Reduction in consumption

= x/5 = 20% of x

**Question28 :**If the length of a rectangle is halved and the breadth is tripled, by how much % does the area of the rectangle increase?

Option 1 : 20%

Option 2 : 30%

Option 3 : 50%

Option 4 : 100%

Answer : C

**Explanation**: New area = l/2 * 3b = 3lb/2

% change

= [((3lb/2)- lb)/lb] * 100

= 50%

**Question29**: Reena scores 80 marks in her first internal maths paper. By how much should she improve her mark in the second internal in order to get an average of 90 in maths?

Option 1 : 100%

Option 2 : 50%

Option 3 : 25%

Option 4 : 20%

Answer : C

**Explanation**: If her average should be 90, she should score 100 in the second internal.

% improvement

= [(100-80)/80] * 100

= 25%

**Question30**: Ravi's salary was reduced by 25%.Percentage increase to be effected to bring the salary to the original level is

Option 1 : 20%

Option 2 : 25%

Option 3 : 33.33%

Option 4 : 30%

Answer : C

**Explanation**: Let Ravi’s salary be x and his new salary be 0.75x.

To bring his salary to the original level, 0.25x should be added.

% increase

= (0.25x/0.75x) * 100

= 33.33%

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