NCERT Class 8 Maths Chapter 13 Direct and Inverse Proportions Exercise 13.1


Chapter 13 Direct and Inverse Proportions Exercise 13.1

Question 1: Following are the car parking charges near a railway station upto
4 hours                       Rs 60
8 hours                       Rs 100
12 hours                     Rs 140
24 hours                     Rs 180
Check if the parking charges are in direct proportion to the parking time.
Answer:
No, 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.

Question 2

Answer:

Question 2 Answer

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:
Let the red pigment that is required to be mixed with 1800 mL be x.

Question 3 Answer

= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 1/75 = x/1800
= 75 × x = 1800 × 1
= x = 1800 × 1/75
= x = 24
Therefore, 24 parts of red pigment requires 1800 mL of base.

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

Question 4 Answer

= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 840/6 = x/5
= 6 × x = 840 × 5
= x = 840 × 5/6
= x = 700
Therefore, 700 bottles will the machine fill in 5 hours.

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?
Answer:
Let the enlarged length of bacteria if the photograph is 20000 times only, be x.

Question 5 Answer

= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 50000/5 = 20000/x
= 50000 × x = 20000 × 5
= x = 20000 × 5/50000
= x = 2
Therefore, if the photograph is enlarged 20000 times only, 2 cm would be its enlarged length.

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 of the ship is 28 m, how long is the model ship?
Answer:
Let the length of model ship be x.

Question 6 Answer

= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 9/x = 1200/2800
= 9 × 2800 = x × 1200
= x = 9 × 2800/1200
= x = 21
Therefore, the length of the model ship is 21 cm.

Question 7: Suppose 2 kg of sugar contains 9 × 106 crystals. How many sugar crystals are there in (i) 5 kg of sugar? (ii) 1.2 kg of sugar?
Answer:
Let the number of sugar crystals in 5 kg sugar be x₁ and the number of sugar crystals in 1.2 kg of sugar be x₂.

Question 7 Answer

i)
= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 2000/9 × 10⁶ = 5000/x₁
= 2000 × x₁ = 9 × 10⁶ × 5000
= x₁ = 9 × 10⁶ × 5000/2000
= x₁ = 45000 × 10⁶/2000
= x₁ = 22.5 × 10⁶
= x₁ = 2.25 × 10⁷
Therefore, the number of sugar crystals in 5 kg sugar is 2.25 × 10⁷.

ii)
= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 2000/9 × 10⁶ = 1200/x₂
= 2000 × x₂ = 9 × 10⁶ × 1200
= x₂ = 9 × 10⁶ × 1200/2000
= x₂ = 108 × 10⁶/20
= 54 × 10⁶/10
= 54 × 10⁵
= 5.4 × 10⁶
Therefore, the number of sugar crystals in 1.2 kg sugar is 5.4 × 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:
Let the distance 72 km covered on the map be x.

Question 8 Answer

= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 1/18 = x/72
= 1 × 72 = x × 18
= x = 72/18
= x = 4
Therefore, the distance covered by Rashmi on the map would be 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 5m long.
Answer:
Let the length of shadow cast by another pole 10 m 50 cm high be x₁. Let the height of a pole which casts a shadow 5 m long be x₂.

Question 9 Answer

i)
= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 560/320 = 1050/x₁
= 560 × x₁ = 320 × 1050
= x₁ = 320 × 1050/560
= x₁ = 600
Therefore, the length of the shadow cast by another pole 10 m 50 cm high is 6 m (600 cm).

ii)
= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 560/320 = x₂/500
= 560 × 500 = 320 × x₂
= x₂ = 560 × 500/320
= x₂ = 875
Therefore, the height of a pole which casts a shadow 5 m long is 8.75 m (875 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:
Let the distance travelled by loaded truck in 5 hours be x.

Question 10 Answer

= x₁/y₁ = x₂/y₂
= x₁y₂ = y₁x₂
= 14/25 = x/300
= 14 × 300 = 25 × x
= x = 14 × 300/25
= x = 168
Therefore, the loaded truck can travel 168 km in 5 hours.

No comments:

Post a Comment

Also read!

Click on any of the below text for additional links:

Class 6

Class 6 Computer Kips Solutions
Class 6 Gul Mohar English Solutions
→ Class 6 Map Pointing Solutions
Class 6 NCERT Civics Solutions
Class 6 NCERT Geography Solutions
Class 6 NCERT History Solutions
Class 6 NCERT Maths Solutions
Class 6 NCERT Science Solutions

Class 7

Class 7 Computer Kips Solutions
Class 7 Gul Mohar English Solutions
English Grammar Class 7
English Writing Skills Class 7
Class 7 Map Pointing Solutions
Class 7 NCERT Civics Solutions
Class 7 NCERT Civics Notes
Class 7 NCERT Civics Extra Questions
Class 7 NCERT Geography Solutions
Class 7 NCERT Geography Notes
Class 7 NCERT Geography Extra Questions
Class 7 NCERT History Solutions
Class 7 NCERT History Notes
Class 7 NCERT History Extra Questions
Class 7 NCERT Maths Solutions
Class 7 NCERT Science Solutions
Class 7 NCERT Science Notes
Class 7 NCERT Science Extra Questions

Class 8

Class 8 Kips Artificial Intelligence Solutions
Class 8 Gul Mohar English Solutions
English Grammar Class 8
English Writing Skills Class 8
Class 8 Map Pointing Solutions
Class 8 NCERT Civics Solutions
Class 8 NCERT Civics Notes
Class 8 NCERT Civics Extra Questions
Class 8 NCERT Geography Solutions
Class 8 NCERT Geography Notes
Class 8 NCERT Geography Extra Questions
Class 8 NCERT History Solutions
Class 8 NCERT History Notes
Class 8 NCERT History Extra Questions
Class 8 NCERT Maths Solutions
Class 8 NCERT Science Solutions
Class 8 NCERT Science Notes
Class 8 NCERT Science Extra Questions
Class 8 NCERT Science Exemplar
Class 8 NCERT Science MCQs

Class 9

Class 9 Kips Artificial Intelligence Solutions
Class 9 Map Pointing Solutions
Class 9 NCERT Civics Solutions
Class 9 NCERT Geography Solutions
Class 9 NCERT History Solutions
Class 9 NCERT Maths Solutions
Class 9 NCERT Science Solutions

Class 10

Class 10 Kips Artificial Intelligence Solutions
Class 10 NCERT English Solutions
→ Class 10 Map Pointing Solutions
Class 10 NCERT Civics Solutions
Class 10 NCERT Civics Notes
Class 10 NCERT Civics Extra Questions
Class 10 NCERT Geography Solutions
Class 10 NCERT Geography Notes
Class 10 NCERT Geography Extra Questions
Class 10 NCERT History Solutions
→ Class 10 NCERT History Notes
Class 10 NCERT History Extra Questions
Class 10 NCERT Maths Solutions
Class 10 NCERT Science Solutions
Class 10 NCERT Science Notes
Class 10 NCERT Science Extra Questions

Computer Languages

Python Basics

Extra Activities

Extra Activities

Extra Knowledge

Extra Information
General Knowledge
Historical Places in India
Latest technology
Physical Sciences
Facts

• Mathematics quick links
Mathematical Terms
Maths Tricks

Home Top