# class 8 maths chapter 13 exercise 13.1 solutions

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## CBSE NCERT Class 8 Maths Chapter 13 Exercise 13.1 Solution (2022

NCERT Solutions for Class 8 Maths Chapter 13 Exercise 13.1 (Ex. 13.1) Direct and Inverse Proportions Hindi English Medium for 2022-2023.

NCERT Solutions for Class 8 Maths Chapter 13 Exercise 13.1 (Ex. 13.1) Direct and Inverse Proportions in Hindi and English Medium for CBSE Exams 2022-2023 free. All the questions of exercises are also solve in videos. Please take help of videos if any doubt in PDF solutions. In Class 8 Maths exercise 13.1 we will do the questions related to direct proportions and its application. If someone is facing problem to access the contents of Tiwari Academy, please contact us for help.

## Class 8 Maths Chapter 13 Exercise 13.1 Solution

Class: 8 Mathematics

Chapter: 13 Direct and Inverse Proportions

Exercise: 13.1 PDF and Videos Solutions

### CBSE NCERT Class 8 Maths Chapter 13 Exercise 13.1 Solution in Hindi and English Medium

Class 8 Maths Chapter 13 Exercise 13.1 Solution in English Medium

Class 8 Maths Chapter 13 Exercise 13.1 Solution in Hindi Medium

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### Class 8 Maths Chapter 13 Exercise 13.1 Solution in Videos

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Class 8 Maths Chapter 13 Exercise 13.1 Solution

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Class 8 Maths Chapter 13 Exercise 13.1 Explanation

### Variation

If two quantities depend on each other in such a way that the change in one results in a corresponding change in the other, then the two quantities are said to be in variation.

There are many situations in our daily life where the variation in one quantity brings a variation in the other.

Example:

(i) More articles will cost more.

(ii) More is the money deposited in a bank, more is the interest earned in a fixed period,

(iii) More is the distance covered by a car, more is the petrol consumed by it.

(iv) More is the speed of a car, less is the time taken to cover a fixed distance.

(v) More is the number of workers at a work, less is the time taken to complete the work.

### Direct Proportion (or Direct Variation)

Two quantities x and y are said to be in direct proportion if whenever the value of x increases (or decreases), then the value of y increases (or decreases) in such a way that the ratio x/y remains constant.

Thus, x and y are in direct proportion, if x/y = k, where k is a constant, i.e.,

X1/y1 = x2/y2 = x3/y3 = ……= k

Example (i), (ii) and (iii) given above are the cases of direct proportion.

Remark: of y increases (or decreases) in such a way that the ratio remains constant. When x and y are in direct proportion, we also say that x and y have a direct variation.

### A car covers 432 km in 36 litres of petrol. How much distance would it cover in 25 litres of petrol.

### How do you solve direct variations?

### What is a real life example of direct variation?

### How do you define direct variation?

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

Exercise 13.1 Chapter 13 : NCERT Solutions for Class 8 Maths Chapter 14 Factorisation Ex 14.1 are given here for free which the students can download and clear their doubts instantly.

NCERT SolutionsNCERT Class 8NCERT 8 MathsChapter 13: Direct Inverse ProportionsExercise 13.1

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

NCERT Solutions for Class 8 Maths Chapter 13, Direct and Inverse Proportions is a combination of questions and answers for all textbook problems, prepared by BYJU’S subject experts. These NCERT Class 8 exercise questions make students familiar with the various concepts. CBSE Chapter 13 comprises standard questions which consist of various topics carrying different marks, so students must be well aware of all concepts to score well. Download mathematics NCERT Solutions and sharpen your skills. These NCERT solutions are an easy way to practise and learn the concepts covered in Class 8 Chapter 13.

### Download PDF of NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Exercise 13.1

### Access Other Exercise Solutions of Class 8 Maths Chapter 13 Direct and Inverse Proportions

Exercise 13.2 Solutions : 11 Questions (Long answers)

### Access Answers to NCERT Class 8 Maths Chapter 13 Direct and Inverse Proportions Exercise 13.1 Page number 208

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.**

**Solution:**

Charges per hour: C1 = 60/4 = Rs. 15

C2 = 100/8 = Rs. 12.50

C3 = 140/12 = Rs. 11.67

C4 = 180/24 = Rs.7.50

Here, the charges per hour are not same, i.e., C1 ≠ C2 ≠ C3 ≠ C4

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

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:

Let the ratio of parts of red pigment and parts of base be a/b .

Case 1: Here, a1 = 1, b1 = 8

a1/b1 = 1/8 = k (say)

Case 2: When a2 = 4 , b2 = ?

b2 = a2/k = 4/(1/8) = 4×8 = 32

Case 3: When a3 = 7 , b3 = ?

b3 = a3/k = 7/(1/8) = 7×8 = 56

Case 4: When a4 = 12 , b4 =?

b4 = a4/k = 12/(1/8) = 12×8 = 96

Case 5: When a5 = 20 , b5 = ?

b5 = a5/k = 20/(1/8) = 20×8 = 160

Combine results for all the cases, we have

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 parts of red pigment mix with 1800 mL base be x.

Since it is in direct proportion.

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

**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 number of bottles filled in five hours be x.

Here ratio of hours and bottles are in direct proportion.

6x = 5×840 x = 5×840/6 = 700

Hence machine will fill 700 bottles in five hours.

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**:

Let enlarged length of bacteria be x .

Actual length of bacteria = 5/50000 = 1/10000 cm = 10-4 cm

Here length and enlarged length of bacteria are in direct proportion.

x= 2cm

Hence the enlarged length of bacteria is 2 cm.

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?

**Solution**:

Let the length of model ship be x .

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

x = 21 cm

Hence length of the model ship is 21 cm.

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:**

(i) Let sugar crystals be x.

Here, weight of sugar and number of crystals are in direct proportion.

=

Hence the number of sugar crystals is

(ii) Let sugar crystals be x.

Here weight of sugar and number of crystals are in direct proportion.

=

Hence the number of sugar crystals is 5.4×106

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 distance covered in the map be x.

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

x = 4 cm

Hence distance covered in the map is 4 cm.

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.

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

NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Class 8 Maths Direct and Inverse Proportions Exercise 13.1 Class 8 Maths Direct and Inverse Proportions Exercise 13.2 Direct and Inverse Proportions Class 8 Extra Questions NCERT Solutions for Class 8 Maths Chapter 13 Direct and Inverse Proportions Exercise 13.1 Ex 13.1 Class […]

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

October 4, 2019 by Sastry CBSE

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

Class 8 Maths Direct and Inverse Proportions Exercise 13.1

Class 8 Maths Direct and Inverse Proportions Exercise 13.2

Direct and Inverse Proportions Class 8 Extra Questions

**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.

Solution:

We have the ratio of time period and the parking charge.

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.

Solution:

Let the number to be filled in the blanks be a, b, c and d respectively.

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.

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.

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?

Solution:

Let the actual length be x 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 the required length of the model ship be x m.

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.

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.

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

Guys, does anyone know the answer?