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

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## 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:
(1) If the number of articles purchased increases, the total cost also increases.
(2) More the money deposited in a bank, more is the interest earned.
(3) As the speed of a vehicle increases, the time taken to cover the same distance decreases.
(4) For a given job, more the number of workers, less will be the time taken to complete the work.

### 13.2 Direct Proportion

If the cost of 1 kg of sugar is Rs 18, then what would be the cost of 3 kg sugar? It is Rs 54. Similarly, we can find the cost of 5 kg or 8 kg of sugar.
Observe that as 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 litres, i.e., three times of 4 litres, the distance travelled will also be three times of 60 km. In other words, when the petrol consumption becomes three-fold, the distance travelled is also three fold the previous one. Let the consumption of petrol be x litres and the corresponding distance travelled be y km .

### 13.3 Inverse Proportion

Two quantities may change in such a manner that if one quantity increases, the other quantity decreases and vice versa. For example, as the number of workers increases, time taken to finish the job decreases. Similarly, if we increase the speed, the time taken to cover a given distance decreases. To understand this, let us look into the following situation. Zaheeda can go to her school in four different ways. She can walk, run, cycle or go by car.Observe that as the speed increases, time taken to cover the same distance decreases. As Zaheeda doubles her speed by running, time reduces to half. As she increases her speed to three times by cycling, time decreases to one third. Similarly, as she increases her speed to 15 times, time decreases to one fifteenth. (Or, in other words the ratio by which time decreases is inverse of the ratio by which the corresponding speed increases). Can we say that speed and time change inversely in proportion? Let us consider another example. A school wants to spend Rs 6000 on mathematics textbooks. How many books could be bought at Rs 40 each? Clearly 150 books can be bought. If the price of a textbook is more than Rs 40, then the number of books which could be purchased with the same amount of money would be less than 150. Observe the following table.

### Smartur

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