NCERT Exemplar Class 8 Maths Unit 10 Direct and Inverse Proportions

Candidates can download NCERT Exemplar Class 8 Maths Unit 10 from this page. The exemplar has been provided by the National Council of Educational Research & Training (NCERT) and the candidates can check it from below for free of cost. It contains objective, very short answer type, short answer type, and long answer type questions. Along with it, the answer for each question has also been provided. From the NCERT Exemplar Class 8 Maths Unit 10, candidates can understand the level and type of questions that are asked in the exam.

NCERT Exemplar Class 8 Maths Unit 10 Direct and Inverse Proportions

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NCERT Class 8 Maths Unit 10 is for Direct and Inverse Proportions. The type of questions that will be asked from NCERT Class 8 Maths Unit 10 are displayed in the below provided NCERT Exemplar Class 8 Maths Unit 10. With the help of it, candidates can prepare well for the examination.

Main Concepts and Results

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Two quantities x and y are said to be in direct proportion if they increase or decrease together in such a manner that the ratio oftheir corresponding values remains constant. That is, x y = k where k is a positive number, if x and y are in direct proportion or vary directly. In case of direct proportion, if y1, y2 are the values of y corresponding to the values x1, x2 of x respectively, then

Two quantities x and y are said to be in inverse proportion if an increase in x causes a proportional decrease in y and vice-versa, in such a manner that the product of their corresponding values remains constant. That is, xy = k where k is a positive number, if x and y are in inverse proportion. In this case, if y1, y2 are the values of y corresponding to the values x1, x2 of x respectively, then x1 y1= x2 y2 or

Quantities increasing or decreasing together need not always be in direct proportion, same in the case of inverse proportion.
When two quantities x and y are in direct proportion (or vary directly), they are written as x ∝ y. Symbol “∝” stands for ‘is proportional to’.
When two quantities x and y are in inverse proportion (or vary inversely) they are written as x ∝ 1 /y .

Solved Examples

In examples 1 to 3, there are four options out of which one is correct.
Choose the correct answer,

In examples 4 to 6, fill in the blanks to make the statements true.

In examples 7 to 9, state whether the statements are true (T) or false (F):

Think and Discuss

1. What will happen if question is: If 30 men can reap a field in 17 days, then 10 men reap the field in how many days?

2. In the questions of men and work we always use indirect variation. Now think of some situation related to men where direct variation will be used, e.g. If maximum 15 men can travel by three cars, then find minimum maximum number of cars required for (a) 25 men (b) 38 men.