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NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8 PDF Download

Exercise 13.1 

Question 1: 

Following are the car parking charges near a railway station up to: 

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Check if the parking charges are in direct proportion to the parking time. 

Answer 1: 

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Here, the charges per hour are not same, i.e., C1 ≠ C≠ C3 ≠C4

Therefore, the parking charges are not in direct proportion to the parking time.

Question 2: 

A mixture of paint is prepared by mixing 1 part of red pigments with 8 parts of base. In the following table, find the parts of base that need to be added.

Parts of red pigment

1

4

7

12

20

Parts of base

8


Answer 2: 

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Parts of red pigment

1

4

7

12

20

Parts of base

8

32

56

96

160

 

Question 3: 

In Question 2 above, if 1 part of a red pigment requires 75 mL of base, how much red pigment should we mix with 1800 mL of base? 

Answer 3: 

Let the parts of red pigment mix with 1800 mL base be x

Parts of red pigment

1

X

Parts of base

75

1800

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, with base 1800 mL, 24 parts red pigment should be mixed.

Question 4: 

A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours? 

Answer 4: 

Let the number of bottles filled in five hours be x.

Hours

1

X

Bottles

75

1800

 

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, the number of bottles filled in five hours be 700.

Question 5: 

A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown In the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Answer 5: 

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Length

5

X

Enlarged length

50,000

20,000

Here length and enlarged length of bacteria are in direct proportion

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Question 6: 

In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length if the ship is 28 m, how long is the model ship? 

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Answer 6: 

Let the length of model ship be x

Length of actual ship (in m)

12

28

Length of model ship (in cm)

9

X

Here length of mast and actual length of ship are in direct proportion

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, the length of the model ship is 21 cm.

Question 7: 

Suppose 2 kg of sugar contains 9 x 106 crystals. How many sugar crystals are there in 

(i) 5 kg of sugar? 

(ii) 1.2 kg of sugar? 

Answer 7: 

Let sugar crystals be x.

Weight of sugar (in kg)

2

5

No. of crystals

9x106

X

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, the number of sugar crystals is 2.25 x 107.

(ii) 

Let sugar crystals be x.

Weight of sugar (in kg)

2

1.2

No. of crystals

9x106

X

 NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, the number of sugar crystals is 5.4 x 106.

Question 8: 

Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map? 

Answer 8: 

Let distance covered in the map be x.

Actual distance (in km)

18

72

Distance covered in map (in cm)

1

X

Here actual distance and distance covered in the map are in direct proportion.

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, distance covered in the map is 4 cm

Question 9: 

A 5 m 60 cm high vertical pole casts a shadow 3 m 20 cm long. Find at the same time 

(i) the length of the shadow cast by another pole 10 m 50 cm high 

(ii) the height of a pole which casts a shadow 5 m long. 

Answer 9: 

Here height of the pole and length of the shadow are in direct proportion.

And 1 m = 100 cm

5 m 60 cm = 5 x 100 + 60 = 560 cm

3 m 20 cm = 3 x 100 + 20 = 320 cm

10 m 50 cm = 10 x 100 + 50 = 1050 cm

5 m = 5 x 100 - 500 cm

(i) Let the length of the shadow of another pole be x.

Height of pole (in cm)

560

1050

Length of shadow (in cm)

320

X

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, the length of the shadow of another pole be 6m.

Let the hight of the pole be x.

Height of pole (in cm)

560

x

Length of shadow (in cm)

320

500

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

Hence, the hight of the pole be 8m 75 cm

Question 10: 

A loaded truck travels 14 km in 25 minutes. If the speed remains the same, how far can it travel in 5 hours? 

Answer 10: 

Let distance covered in 5 hours be .r km.

 1 hour = 60 minutes

5 hours = 5 x 60 = 300 minutes

Distance (in km]

14

X

Time (in minutes)

25

300

Here distance covered and time in direct proportion.

NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

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FAQs on NCERT Solutions (Ex - 13.1) - Direct and Inverse Proportions - Class 8

1. What are direct and inverse proportions?
Ans. Direct proportion is a relationship between two variables where an increase in one variable leads to a corresponding increase in the other variable. Inverse proportion is a relationship between two variables where an increase in one variable leads to a corresponding decrease in the other variable.
2. How can we identify if two variables are in direct or inverse proportion?
Ans. To identify if two variables are in direct or inverse proportion, we can use the formula y = kx, where y and x are the variables and k is a constant. If k is positive, then the variables are in direct proportion. If k is negative, then the variables are in inverse proportion.
3. What are some real-life examples of direct and inverse proportion?
Ans. Examples of direct proportion include the relationship between speed and distance traveled, where an increase in speed leads to an increase in distance covered. Examples of inverse proportion include the relationship between the number of workers and the time taken to complete a task, where an increase in the number of workers leads to a decrease in the time taken to complete the task.
4. What is the difference between direct and inverse proportion?
Ans. The main difference between direct and inverse proportion is the relationship between the variables. In direct proportion, an increase in one variable leads to a corresponding increase in the other variable, while in inverse proportion, an increase in one variable leads to a corresponding decrease in the other variable.
5. How can we solve problems related to direct and inverse proportions?
Ans. To solve problems related to direct and inverse proportions, we can use the formula y = kx, where y and x are the variables and k is a constant. We can then use the given information to calculate the value of k, and use it to find the value of the unknown variable. It is important to ensure that the units of the variables are the same before applying the formula.
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