NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

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NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions

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

Ex 13.1 Class 8 Maths Question 1.
Following are the car parking charges near a railway station up to.
4 hours – ₹ 60
8 hours – ₹ 100
12 hours – ₹ 140
24 hours – ₹ 180
Check if the parking charges are in direct proportions to the parking time.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q1
Solution:
We have the ratio of time period and the parking charge.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q1.1
Hence the given quantities are not directly proportional.

Ex 13.1 Class 8 Maths 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.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q2
Solution:
Let the number to be filled in the blanks be a, b, c and d respectively.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q2.1

Ex 13.1 Class 8 Maths 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?
Solution:
Let the required red pigment be x part.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q3
Hence, the required amount of red pigment = 24 parts.

Ex 13.1 Class 8 Maths Question 4.
A machine in a soft drink factory fills 840 bottles in six hours. How many bottles will it fill in five hours?
Solution:
Let the required number of bottles be x.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q4
Hence the required number of bottles = 700.

Ex 13.1 Class 8 Maths 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 for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q5
Solution:
Let the actual length be x cm.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q5.1

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q5.2

Ex 13.1 Class 8 Maths 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?
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q6
Solution:
Let the required length of the model ship be x m.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q6.1

Ex 13.1 Class 8 Maths 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?
Solution:
Let x be the number of sugar crystals needed.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q7

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q7.1

Ex 13.1 Class 8 Maths Question 8.
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road of 72 km. What would be her distance covered in the map?
Solution:
Let the required distance be x km.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q8
Hence the distance covered in the map = 4 cm.

Ex 13.1 Class 8 Maths 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.
Solution:
(i) Let the required length of shadow be x m.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q9

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q9.1

Ex 13.1 Class 8 Maths 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?
Solution:
Let the required distance be x km.
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 Q10
Hence the required distance = 168 km.

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-1

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-2

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-3

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-4

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-5

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-6

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-7

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 q-8

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