Comparing Quantities Test

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Comparing Quantities Test - 6

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Question 1
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The area of a rectangular table is 720 cm². A book covers of the area of the table. The breadth to length ratio of the book is 4 : 5 . Find the perimeter of the book.

A
71 cm

B
64 cm

C
54 cm

D
45 cm

Solution

Area of the book = 720 x= 180 cm²Let the length of the book be 5x, and the breadth of the book be 4x.
Then, 4x x 5x = 180

x²=

x = 3
Length = 5 x 3 = 15 cm
Breadth = 4 x 3 = 12 cm
Perimeter = 2(15 + 12)
= 54 cm
Question 2
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Radha needed milk for a family function. She ordered 60 L of milk. What percentage of the total milk quantity is 40 cm³?

A
0.0067%

B
0.067%

C
0.67%

D
6.7%

Solution

1 cm³ = 0.001 litre
1 litre = 1000 cm³
60 litres = 60,000 cm³
Required percentage =
= 0.0667%
Question 3
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250% of a motorbike's weight is equal to 1000 kg. What is the bike's weight (in kg)?

A
250 kg

B
300 kg

C
400 kg

D
500 kg

Solution

Let bike's weight be x.

= 1000

x = = 400 kg
Question 4
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Following are the steps involved in finding the percentage values of the ratio 21 : 14 : 15. Arrange them in order from first to last.

(a) Fractional part

(b) Percentage = 42% : 28% : 30%

(c) Sum of 21, 14 and 15 = 21 + 14 + 15 = 50

(d)

(e) 21 : 14 : 15 = 42% : 28% : 30%

A
(a) - (b) - (c) - (d) - (e)

B
(c) - (a) - (d) - (b) - (e)

C
(b) - (c) - (d) - (e) - (a)

D
(e) - (a) - (d) - (b) - (c)

Solution

The correct order is:
(c) Sum of 21, 14 and 15 = 21 + 14 + 15 = 50

(a) Fractional part =

(d)

(b) Percentage = 42% : 28% : 30%

(e) 21 : 14 : 15 = 42% : 28% : 30%
Question 5
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A family has 3 members - Q, R and S. Ages of Q and R are in the respective ratio of 5 : 9. Ages of R and S are in the respective ratio of 8 : 3. The oldest person among them is 72 years old. Find the difference between the ages of the oldest and the youngest persons in the family.

A
15 years

B
27 years

C
45 years

D
72 years

Solution

According to the question:
Q : R = 5 : 9 ...(i)
R : S = 8 : 3 ...(ii)

Multiply (i) by 8 and (ii) by 9 to get the common ratio of Q, R and S.

The new ratio becomes
Q : R : S = 40 : 72 : 27
Let the ages of Q, R and S be 40x, 72x and 27x, respectively.
The age of the oldest person is 72.
We can see that R is the oldest.
Now, 72x = 72, i.e. x = 1

Age of Q = 40
Age of R = 72
Age of S = 27
Required difference = 72 - 27 = 45
Question 6
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is equal to

A
1.5

B
5

C
10.5

D
15.2

Solution

( x x 1000 g) ÷ ( x x 1000 g)

30 ÷ 20 = 1.5
Therefore, option 1 is the correct answer.
Question 7
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Cost of a table is 20% more than that of a chair. By what percentage is table costlier than chair?

A
10%

B
20%

C
25%

D
30%

Solution

The first part of the question tells us that cost of the table is 20% more than that of the chair. It means that the table is 20% costlier than chair.
Question 8
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Raja sets out on a road trip to a place 500 km away. He has completed 25% of his journey. How much distance has he already covered?

A
25 km

B
50 km

C
100 km

D
125 km

Solution

25% of 500

x 500 = 125 km

Raja has covered a distance of 125 km.
Question 9
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Priya bought one dozen eggs for Rs. 7. She sold half a dozen eggs for Rs. 9. Find the profit or loss percentage on one egg. (Rounded to the nearest whole number)

A
84% profit

B
97% loss

C
100% loss

D
157% profit

Solution

CP of 12 eggs = Rs. 7

CP of 1 egg = Rs.

SP of 6 eggs = Rs. 9

SP of 1 egg = Rs.

Gain = SP - CP =
=

Gain % = = = 157%
Question 10
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What percent of the following figure is shaded?

A
78

B
52

C
48

D
24

Solution

Total number of squares = 100
Number of shaded squares = 52

Percentage shaded part = x 100 = 52%
Question 11
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Which among the following is an incorrect combination?

A
SP = Rs. 120, CP = Rs. 80, Profit = 50%

B
SP = Rs. 100, CP = Rs. 80, Profit = 25%

C
SP = Rs. 80, CP = Rs. 100, Loss = 20%

D
SP = Rs. 70, CP = Rs. 50, Profit = 50%

Solution

CP = Rs. 50 and SP = Rs. 70
Profit = x 100
Profit = 70 - 50 = 20
Profit = x 100 = 40%
Question 12
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If the ratio of simple interest to principle is 4 : 25, and the rate of interest and time are numerically equal, then find the rate of interest and time.

A
r = 3%, t = 3 years

B
r = 8%, t = 8 years

C
r = 4%, t = 4 years

D
r = 5%, t = 5 years

Solution

Let the simple interest and principle, respectively, be 4x and 25x.
Simple interest =
r = t
4x =
400x = 25x x r²

r²=
r²= 16
r = 4%
t = 4 years
Question 13
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What percent of 2.4 kg is 180 g?

A
7.5%

B
8%

C
9.5%

D
10%

Solution

2.4 kg = 2000 + 400 = 2400 g
Required percentage = x 100 = 7.5%
Question 14
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The ratio of two numbers is 4 : 5. If the first number is increased by 25 and the second is decreased by 5, then the terms of the ratio become the same. Find the two original numbers.

A
40 and 90

B
80 and 100

C
100 and 120

D
120 and 150

Solution

Let the original numbers be 4x and 5x.
Terms of the ratio become the same, therefore the numbers become equal.
4x + 25 = 5x - 5
5x - 4x = 25 + 5
x = 30

So, the numbers are:
4x = 4 x 30 = 120
5x = 5 x 30 = 150
Question 15
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In an exam, the passing score is 40%. A student scores 30% and fails by 30 marks. Find the total marks of the exam.

A
100

B
200

C
300

D
150

Solution

Passing score is 40%, and the student scores 30% and fails by 30 marks.
So, 40% - 30% = 10%
10% of total marks = 30
100% of total marks = 30 x 10 = 300 marks
Question 16
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A contractor employs 240 men to do a piece of work in 80 days. If after 10 days, the allotted time is reduced by 10 days, then how many more men does he need?

A
60

B
20

C
50

D
40

Solution

Contractor employs 240 men to do a piece of work in 80 days, so total work to be done =
It is given that they work for 10 days.
So, work done in 10 days =

Let us suppose, he employs x more men.
So now, 240 + x men will work for 60 days to complete the work.

x = 40
Question 17
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A shopkeeper sold two fans that costed him Rs. 2000 each, making a profit of 8% on one of them. If he made a total profit of 5% on the whole transaction, then for how much did he sell the second fan?

A
Rs. 2000

B
Rs. 2040

C
Rs. 2100

D
Rs. 2300

Solution

Total cost = 2000 + 2000 = Rs. 4000
Profit = _x 100
8% profit on one = x 2000 = Rs. 160
5% profit on the whole = x 4000 = Rs. 200
Selling price of first fan = 2000 + 160 = Rs. 2160
Selling price of both the fans together = Rs. 4200

Let the selling price of the second fan be Rs. x.
2160 + x = 4200
x = 4200 - 2160
x = Rs. 2040
Question 18
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If a person sells a basketball for Rs. 260, he will make a profit equal to one-tenth of the selling price. Find the percentage gain he will make if its sold for Rs. 280.

A
17.2%

B
18.5%

C
19.4%

D
19.7%

Solution

SP = Rs. 260
Gain = One-tenth of the selling price = .
CP = 260 - 26 = Rs. 234

Now, when it is sold for Rs. 280, then:
Profit = 280 - 234 = Rs. 46

Profit percentage = × 100 = 19.7%
Question 19
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Two booksellers, John and Lisa, each bought a box of comic books, containing 15 copies per box, from different vendors. John got the box for Rs. 350, while Lisa got it for Rs. 320. If John sold each book for Rs. 30 and Lisa sold each book for Rs. 28, then who made more profit percentage and by how much?

A
John, 2.68%

B
Lisa, 3.65%

C
John, 3.65%

D
Lisa, 2.68%

Solution

John and Lisa each bought a box of comic books, containing 15 copies per box, from different vendors. John got the box for Rs. 350 and Lisa got it for Rs. 320.
John sold each book for Rs. 30, so 15 books were sold for 15 x 30 = Rs. 450
Lisa sold each book for Rs. 28, so 15 books were sold for = 15x28 =Rs.420
Profit made by John = Rs. 450 - Rs. 350

Profit % for John = x 100 = 28.57%

Profit made by Lisa = 420 - 320 = Rs. 100

Profit % for Lisa = x 100 = 31.25%

So, Lisa made more profit.
Difference = 31.25 - 28.57= 2.68%
Question 20
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Sahil has 56 chocolates. He wants to divide them in the ratio of 2 : 5 between his friends Kashish and Avi, respectively. How many chocolates will both friends get individually?

A
Kashish: 13, Avi:43

B
Kashish: 14, Avi:42

C
Kashish: 15, Avi:41

D
Kashish: 16 , Avi: 40

Solution

Total number of chocolates = 56
Number of chocolates Kashish gets = 56 x = 16
Number of chocolates Avi gets = 56 x = 40
Question 21
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An organisation has 786 employees, out of which % are above 30 years and the rest are below 30 years of age. Find out the number of employees which are above 30 years.

A
150

B
146

C
135

D
131

Solution

Total number of employees = 786
Percentage of employees above 30 years of age = % = %
Number of employees above 30 years of age = 786 x ( x )
= 786 x = 131
Question 22
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In a marathon, out of a total of 14,000 students, 5600 wore a blue-coloured jerseys which bore the motto Save Water. What percent of students were wearing blue jerseys?

A
45%

B
40%

C
39%

D
30%

Solution

Percentage of students who were wearing blue jerseys

= = 40%
Question 23
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To be selected in the team, a player should score 40% on his fitness test. Hari fails the test by 40 points as he obtains only 120. Find the maximum points of the test.

A
400

B
475

C
590

D
685

Solution

Let the maximum points of the test be a.

x a = 160

40a = 16,000

a =
a = 400

Question 24

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Joy, an employee of XYZ Ltd., goes on a business trip and takes along Rs. 25,000 with him. He spends money on food and accommodation, out of which some amount will be reimbursed by the company to him. By looking at the following table, find out how much money does he have when he returns?

Date	Money spent on food and accommodation	Money reimbursed
21.03.2018	Rs. 7500	Rs. 6500
25.03.2018	Rs. 2500	Rs. 1500

Rs. 23,000

Rs. 24,000

Rs. 25,000

Rs. 26,000

Solution

Total money with Joy = Rs. 25,000

Total money spent = Rs. (7500 + 2500) = Rs. 10,000

Total money reimbursed by the company = Rs. (6500 + 1500) = Rs. 8000

Money left with Joy = Rs. (25,000 - 10,000) + 8000 = Rs. 23,000

Question 25

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Match the following:

Column I	Column II
i. Atul sells his bike for Rs. 25,000 at a profit of 25%. The cost price of the bike was	P. 12
ii. Ram deposits a certain sum of money in bank at the rate of 4% for 4 years, and the interest earned is Rs. 420. Find the amount deposited by Ram.	Q. 2625
iii. The ratio of boys to girls in a classroom is 4 : 9, and the number of girls is 27. How many boys are there in the class?	R. 20000

i - Q, ii - P, iii - R

i - R, ii - P, iii - Q

i - R, ii - Q, iii - P

i - Q, ii - R, iii - P

Solution

i. SP = Rs. 25,000
Profit % = 25%

Profit % =

25% =

25CP = 25,00,000 - 100CP
125CP = 25,00,000
CP = Rs. 20,000

ii. SI = Rs. 420
R = 4%
T = 4 years

= SI

P = = Rs. 2625

iii. Boys : Girls = 4 : 9
Let the numbers of boys and girls be 4x and 9x, respectively.
Now, 9x = 27.
x = 3
Boys = 4x = 4 x 3 = 12

Question 26
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State whether the following are true or false:

1. Yash has a total of 2150 chocolates. He eats 44% of them. He has 1300 chocolates left.
2. In a college, there are 70 boys, 75 girls, 98 female teachers, and 37 male teachers. The percentage of total females in the whole college is 59%.
3. Roshan, a whole-seller, bought 1250 kg of bananas at Rs. 25 per kg. He sold them at Rs. 28 per kg and made a profit of 12%.

A
1-False, 2-False, 3-True

B
1-True, 2-False, 3-True

C
1-True, 2-True, 3-True

D
1-False, 2-True, 3-False.

Solution

1. Yash has a total of 2150 chocolates. He eats 44% of them. He has 1300 chocolates left.
Total chocolates = 2150

He eats = 946 chocolates

Chocolates left = 2150 - 946 = 1204, so 1 is false.

2. In a college, there are 70 boys, 75 girls, 98 female teachers, and 37 male teachers. The percentage of total females in the whole college is 59%.
Total number of people = 70 + 75 + 98 + 37 = 280
Number of females = 173
Now, let a be the percent of females in the college

= 173

280a = 17,300

a =

a = 61.8%, so 2 is false.

3. Roshan, a whole-seller, bought 1250 kg of bananas at Rs. 25 per kg. He sold them at Rs. 28 per kg and made a profit of 12%.
Total number of bananas = 1250 kg
CP = 1250 x 25 = Rs. 31,250
SP = 1250 x 28 = Rs. 35,000
Profit = SP - CP = 35,000 - 31,250 = Rs. 3750

Profit percentage = = 12%, so 3 is true.
Question 27
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Which of the following statements is correct?

Statement-1: XYZ Ltd. has 440 employees, out of which 110 are in Marketing department. The ratio of number of employees in Marketing department to that in entire organisation is 4 : 1.
Statement-2: In a town of 100 people, 4 out of 10 people own a car. The percentage of people who own a car is 80%.

A
Both statement 1 and statement 2 are correct.

B
Both statement 1 and statement 2 are incorrect.

C
Only statement 1 is correct.

D
Only statement 2 is correct.

Solution

(1) Total number of employees = 440
Total number of employees in Marketing Department = 110
So, required ratio = 110 : 440 = 11 : 44 = 1 : 4
(2) Number of people who own a car = = 40
So, percentage of people who own a car is 40%.
Question 28
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Directions: In this problem, a question is asked followed by three statements, numbered (i), (ii) and (iii). Read all the statements carefully and decide which of them is/are required to answer the question.

What is the principal?

(i) Total simple interest on the sum is Rs. 100.
(ii) Total simple interest on the sum is Rs. 500 for 5 years.
(iii) The rate of interest is 5% per annum.

A
Both (i) and (ii)

B
Both (ii) and (iii)

C
All of them

D
Any two of the three

Solution

Both ii and iii are required.
Given: SI = Rs. 500
R = 5%
T = 5 years

SI =
P = Rs. 2000
Question 29
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Fill in the blanks:

1. The prices of 4 kg of apples and 5 kg of mangoes are Rs. 28 and Rs. 45, respectively. Then, total price of 1 kg of apples and 1 kg of mangoes will be ___A____.
2. The ratio of number of benches to total number of furniture items is ____B____, if the numbers of benches and tables are 12 and 24, respectively.
3. If the distance between Town A and Town B is 360 km and a car takes 18 hours to cover that distance, then in 22 hours, it will cover a distance of ___C____.

A
A- Rs. 16, B- 1 : 3, C- 440 km

B
A- Rs. 15, B- 2 : 3, C- 440 km

C
A- Rs. 16, B- 1 : 2, C- 480 km

D
A- Rs. 17, B- 4 : 9, C- 440 km

Solution

1. Price of 4 kg of apples = Rs. 28

Price of 1 kg of apples = Rs. 7

Price of 5 kg of mangoes = Rs. 45

Price of 1 kg of mangoes = Rs. 9

Then, total price of 1 kg of apple and 1 kg of mango will be Rs. (7 + 9) = Rs. 16.

2. The numbers of benches and tables are 12 and 24, respectively. Total number of furniture items = 24 + 12 = 36

Required ratio =

3. Distance covered by car in 18 hours = 360 km

Distance covered by car in 1 hour = Km.

Distance covered by car in 22 hours = 22 x 20 = 440 km