Direct and Inverse Proportions Test

Result

Direct and Inverse Proportions Test - 10

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Weekly Quiz Competition

Question 1
1 / -0

A car travels 34 km in 2 L of petrol. If the car travels 192.1 km, then how much petrol does it consume?

A
11.3 L

B
12.1 L

C
13.9 L

D
14.7 L

Solution

Let k be the amount of petrol consumed by the car to travel 192.1 km.

The given information can be represented in the form of a table as:

Distance travelled (km)

34

192.1

Petrol consumed (L)

2

k

It can be seen that,

The greater the distance, the greater will be the amount of petrol consumed.

Therefore, these two quantities are in direct proportion.

Thus, the amount of petrol consumed by the car to travel 192.1 km is 11.3 L.

The correct answer is A.
Question 2
1 / -0

A shopkeeper earns a profit of Rs 2000 by selling 90 music CDs. How much profit can he earn by selling 279 music CDs?

A
Rs 6200

B
Rs 6000

C
Rs 5400

D
Rs 5000

Solution

Let Rs p be the profit that can be earned by the shopkeeper on selling 279 CDs.

The given information can be represented in the form of a table as:

Number of music CDs

90

279

Profit earned (Rs)

2000

p

It can be seen that the greater the number of music CDs sold, the greater will be the profit earned. Therefore, these two quantities are directly proportional to each other.

Thus, the shopkeeper can earn a profit of Rs 6200 on selling 279 music CDs.

The correct answer is A.
Question 3
1 / -0

Rani prepares tea by adding 3 teaspoons of sugar in two cups. How many cups of tea can be prepared by adding 12 teaspoons of sugar?

A
14

B
12

C
8

D
6

Solution

Let n be the number of cups of tea that can be prepared with 12 teaspoons of sugar.

The given information can be represented in the form of a table as:

Number of teaspoons of sugar

3

12

Number of cups

2

n

It can be seen that greater the number of cups of tea, greater will be the number of teaspoons of sugar required. Therefore, these two quantities are in direct proportion.

Thus, 8 cups of tea can be prepared by adding 12 teaspoons of sugar.

The correct answer is C.
Question 4
1 / -0

In which of the following tables are the variables x and y not in direct proportion?

A

x 2.25 4.5 9 27

y 1.25 2.5 5 15

B

x 3 18 6 2.4

y 2.5 10 5 2

C

x 2 8 2.4 16

y 1.5 6 1.8 12

D

x 4.5 1.8 27 10.8

y 1 0.4 6 2.4

Solution

Variables x and y are said to be in direct proportion if, where k is a constant.

Consider the table given in alternative B:

x

3

18

6

2.4

y

2.5

10

5

2

It can be seen that,

Thus, variables x and y are not in direct proportion.

The correct answer is B.
Question 5
1 / -0

Use the following information to answer the next question.

x

12

8

2.8

y

1.4

e

f

What are the respective values of e and f’ in the given table for which the variables x and y are in inverse proportion?

A
4 and 7

B
3 and 2.4

C
2.1 and 6

D
1.3 and 3.5

Solution

The variables x and y are said to be in inverse proportion if xy = k,where k is a constant.

∴ 8 × e = 2.8 × f = 12 × 1.4

Thus, the values of e and f are 2.1 and 6 respectively.

The correct answer is C.
Question 6
1 / -0

Use the following information to answer the next question.

x

c

d

16

y

25.2

5.25

21

What are the respective values of c and d in the given table for which the variables x and y are in direct proportion?

A
19.2 and 4

B
3.4 and 8.5

C
3 and 2.5

D
4 and 8

Solution

Variables x and y are said to be in direct proportion if, where k is a constant.

It can be seen in the given table that,

The variables x and y are in direct proportion. Therefore, we get,

Thus, the values of c and d are 19.2 and 4 respectively.

The correct answer is A.
Question 7
1 / -0

Agroup of 27 students paid Rs 8100 as the entry fee for an amusement park. How many students can enter the amusement park if the total amount paid is Rs 12300?

A
38

B
41

C
43

D
52

Solution

Let n be the number of students that can enter the amusement park on paying Rs. 12300.

The given information can be represented in the form of a table as:

Total entry fee(Rs)

8100

12300

Number of students

27

n

It can be seen that,

The greater the number of students, the greater is the total entry fee. Therefore, these two quantities are in direct proportion.

Thus, 41 students can enter the amusement park on paying Rs 12300.

The correct answer is B.
Question 8
1 / -0

In which of the following tables are the variables a and b not in inverse proportion?

A

a 2.5 3 4 5

b 6 5 3.2 3

B

a 2.4 3 5 6

b 10 8 4.8 4

C

a 2 3.6 4 6

b 9 5 4.5 3

D

a 1.2 1.6 3 6

b 30 22.5 12 6

Solution

The variables a and b are said to be in inverse proportion if ab = k, where k is a constant.

Consider the table given in the alternative A:

a

2.5

3

4

5

b

6

5

3.2

3

It can be seen that,

a₁b₁ = 2.5 × 6 = 15

a₂b₂ = 3 × 5 = 15

a₃b₃ = 4 × 3.2 = 12.8

∴ a₂b₂ ≠ a₃b₃

Thus, variables a and b are not in inverse proportion.

Hence, the correct answer is option A.
Question 9
1 / -0

Use the following information to answer the next question.

Meenakshi bought a ribbon of a certain length. She divides it into nine equal parts such that each part measures 32 cm.

If the same ribbon is divided in such a way that each part measures 24 cm, then how many such parts can be obtained?

A
11

B
12

C
13

D
14

Solution

Let n be the number of parts in which the ribbon can be divided, with each part measuring 24 cm.

The given situation can be represented in the table as:

Length of each part (cm)

32

24

Number of equal parts

9

n

It can be seen that,

The longer is the length of each part, the lesser is the number of parts obtained.

Therefore, the two quantities are inversely proportional.

∴ 32 × 9 = 24 × n

Thus, the ribbon can be divided into 12 equal parts.

The correct answer is B.
Question 10
1 / -0

Use the following information to answer the next question.

The distance between two cities P and Q on the map is 2.7 cm, while the actual distance between them is 675 km.

If the actual distance between two cities R and S is 400 km, then what is the distance between them on the map?

A
1.2 cm

B
1.4 cm

C
1.6 cm

D
1.8 cm

Solution

Let x be the distance between the cities on the map.

We know that,

1 km = 1000 m = 100000 cm

∴ 675 km = 67500000 cm

400 km = 40000000 cm

Therefore, by direct proportion, we get:

Thus, the distance between cities R and S on the map is 1.6 cm.

The correct answer is C.

Question 11

1 / -0

Use the following information to answer the next question.

Manish takesto reach his office in the morning by driving his car at a uniform speed of 60 km/h. In the evening, due to heavy traffic, he can drive his car at a speed of 40 km/h only.

How much time does he take to reach his house in the evening?

1 h

1 h 45 min

2 h

2 h 15 min

Solution

Let t be the time taken by Manish to reach his house in the evening.

The given information can be represented in the form of a table as:

Speed of car (km/h)	60	40
Time taken (h)		t

Now, it can be seen that, lesser the speed of the car, more is the time taken by Manish.

Therefore, these two quantities are inversely proportional.

Thus, he takes 2 h and 15 min to reach his house in the evening.

The correct answer is D.

Question 12
1 / -0

If 24 girls can clean their dining hall in 2 h, then how many girls are required to do the same work in 1 h 30 min?

A
28

B
32

C
36

D
42

Solution

Let n be the number of girls required to clean the dinning hall in 1 h and 30 min.

The given information can be represented in the form of a table as:

Number of girls

24

n

Time taken (h)

2

It can be seen that,

The more the number of girls, the less is the time taken to clean the dining hall.

Therefore, these two quantities are inversely proportional.

∴24 × 2 = n ×

Thus, the number of girls required to clean the dining hall in 1 h and 30 min is 32.

The correct answer is B.

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Distance travelled (km)	34	192.1
Petrol consumed (L)	2	k

Number of music CDs	90	279
Profit earned (Rs)	2000	p

Number of teaspoons of sugar	3	12
Number of cups	2	n

x	2.25	4.5	9	27
y	1.25	2.5	5	15

Direct and Inverse Proportions Test - 10

Result

Direct and Inverse Proportions Test - 10

Score

-

Rank

-

SHARING IS CARING

Question 1

11.3 L

12.1 L

13.9 L

14.7 L

Solution

Question 2

Rs 6200

Rs 6000

Rs 5400

Rs 5000

Solution

Question 3

14

12

8

6

Solution

Question 4

x 2.25 4.5 9 27 y 1.25 2.5 5 15

x 3 18 6 2.4 y 2.5 10 5 2

x 2 8 2.4 16 y 1.5 6 1.8 12

x 4.5 1.8 27 10.8 y 1 0.4 6 2.4

Solution

Question 5

4 and 7

3 and 2.4

2.1 and 6

1.3 and 3.5

Solution

Question 6

19.2 and 4

3.4 and 8.5

3 and 2.5

4 and 8

Solution

Question 7

38

41

43

52

Solution

Question 8

a 2.5 3 4 5 b 6 5 3.2 3

a 2.4 3 5 6 b 10 8 4.8 4

a 2 3.6 4 6 b 9 5 4.5 3

a 1.2 1.6 3 6 b 30 22.5 12 6

Solution

Question 9

11

12

13

14

Solution

Question 10

1.2 cm

1.4 cm

1.6 cm

1.8 cm

Solution

Question 11

1 h

1 h 45 min

2 h

2 h 15 min

Solution

Question 12

28

32

36

42

Solution

x 2.25 4.5 9 27

y 1.25 2.5 5 15

x 3 18 6 2.4

y 2.5 10 5 2

x 2 8 2.4 16

y 1.5 6 1.8 12

x 4.5 1.8 27 10.8

y 1 0.4 6 2.4

a 2.5 3 4 5

b 6 5 3.2 3

a 2.4 3 5 6

b 10 8 4.8 4

a 2 3.6 4 6

b 9 5 4.5 3

a 1.2 1.6 3 6

b 30 22.5 12 6