NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1.
| Board | CBSE |
| Textbook | NCERT |
| Class | Class 8 |
| Subject | Maths |
| Chapter | Chapter 13 |
| Chapter Name | Direct and Inverse Proportions |
| Exercise | Ex 13.1 |
| Number of Questions Solved | 10 |
| Category | NCERT Solutions |
NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Ex 13.1
Ex 13.1 Class 8 Maths Question 1.
Following are the car parking charges near a railway station upto
4 hours ₹ 60
8 hours ₹ 100
12 hours ₹ 140
24 hours ₹ 180
Check if the parking charges are in direct proportion to the parking time.
Solution:
∴ The parking charges are not in direct proportion to the parking time.
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.
Solution:
It is given that parts of red pigment, say x and parts of base, say y are in direct proportion. Therefore, the ratio of the corresponding values of x and y remain constant.
We have, \(\frac { 1 }{ 8 } =\frac { 1 }{ 8 } \).
So, x and y are in direct variation with the constant of variation equal to \(\frac { 1 }{ 8 } \). This means that x is \(\frac { 1 }{ 8 } \) of y and y is eight times of x. Thus, the required entries are \(\frac { 4 }{ 32 } ,\frac { 7 }{ 56 } ,\frac { 12 }{ 96 } ,\frac { 20 }{ 160 } \).
Thus, table becomes
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:
Suppose x parts of red pigment should be mixed with 1800 mL of base. Then the above information can be put in the tabular form as follows:
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:
Suppose x bottles be filled up in five hours. Then the information can be put in the following tabular form :
We observe that the lesser the time consumed, the lesser the number of botdes filled up. So, it is a case of direct variation.
Hence, 700 botdes will be filled up in 5 hours.
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?
Solution:
Suppose x be the enlarged length of the bacteria when its photograph is enlarged 20000 times. Then the information can be put in the following tabular form :
Hence, its enlarged length is 2 cm.
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?
Solution:
Let x metres be the length of the model ship of actual length 28 m. Then the information can be put in the following tabular form :
Hence, the length of the model ship is 21 cm.
Ex 13.1 Class 8 Maths 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?
Solution:
Let x and y crystals are in 5 kg of sugar and 1.2 kg of sugar. Then, the given information can be exhibited in the following tabular form :
Hence, 1.2 kg of sugar contains 5.4 x 106 crystals.
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 for 72 km. What would be her distance covered in the map?
Solution:
Let x cm be the distance covered in the map for the drives of 72 km on a road. Then, the given information can be exhibited in the following tabular form.
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:
Let x m be the length of the pole whose shadow is of length 10 m 50 cm.
Let y m be the length of the pole whose shadow is 5 m long.
Then, the given information can be exhibited in the following tabular form :
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 truck travels x km in 5 hours. Then, the given information can be exhibited in the following tabular form :
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