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

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

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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 Notes - Class 8

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

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

Answer 5: 

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

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