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## NCERT Class 8 Maths Textbook Chapter 13 With Answer Book PDF Free Download

### Chapter 13:Direct And Inverse Proportions

#### 13.1 Introduction

Mohan prepares tea for himself and his sister. He uses 300 mL of water, 2 spoons of sugar, 1 spoon of tea leaves, and 50 mL of milk.

How much quantity of each item will he need, if he has to make tea for five persons?

If two students take 20 minutes to arrange chairs for an assembly, then how much time would five students take to do the same job?

We come across many such situations in our day-to-day life, where we need to see variation in one quantity bringing in variation in the other quantity.

**For example:**(i) If the number of articles purchased increases, the total cost also increases.

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

(iii) As the speed of a vehicle increases, the time taken to cover the same distance decreases.

(iv) For a given job, the more the number of workers, the less will be the time taken to complete the work.

Observe that change in one quantity leads to change in the other quantity. Write five more such situations where a change in one quantity leads to change in another quantity.

How do we find out the quantity of each item needed by Mohan? Or, the time five students take to complete the job?

To answer such questions, we now study some concepts of variation

#### 13.2 Direct Proportion

If the cost of 1 kg of sugar is 36, then what would be the cost of 3 kg sugar? It is 108.

Observe that as the weight of sugar increases, cost also increases in such a manner that their ratio remains constant.

Take one more example. Suppose a car uses 4 litres of petrol to travel a distance of 60 km.

**How far will it travel using 12 litres?**

The answer is 180 km. How did we calculate it? Since petrol consumed in the second instance is 12 liters, i.e., three times 4 liters, the distance traveled will also be three times 60 km.

In other words, when the petrol consumption becomes three-fold, the distance traveled is also threefold the previous one. Let the consumption of petrol be x litres and the corresponding distance travelled be y km.

Author | NCERT |

Language | English |

No. of Pages | 16 |

PDF Size | 2.1 MB |

Category | Mathematics |

Source/ Credits | ncert.nic.in |

### NCERT Solutions Class 8 Maths Chapter 13 Direct And Inverse Proportions

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, a_{1 }= 1, b_{1 }= 8

a_{1}/b_{1} = 1/8 = k (say)

Case 2: When a_{2 }= 4 , b_{2 }= ?

b_{2} = a_{2}/k = 4/(1/8) = 4×8 = 32

Case 3: When a_{3} = 7 , b_{3 }= ?

b_{3 }= a_{3}/k = 7/(1/8) = 7×8 = 56

Case 4: When a_{4 }= 12 , b_{4 }=?

b_{4 }= a_{4}/k = 12/(1/8) = 12×8 = 96

Case 5: When a_{5} = 20 , b_{5 }= ?

b_{5} = a_{5}/k = 20/(1/8) = 20×8 = 160

Combine results for all the cases, we have

NCERT Class 8 Maths Textbook Chapter 13 With Answer Book PDF Free Download