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RD Sharma Solutions for Class 8 Maths Chapter 10: Direct and Inverse variations

The chapter deals with direct proportion and the concept of inverse proportion. The Maths chapter 10 direct and indirect variations cover inverse, proportions, ratio, speed, distance, time, variations, quantity analysis. In direct proportions, two quantities, x and y, are placed, where the value of x increases, the value of y also increases. Therefore, it is said to be a direct proportion.

A direct proportion is represented as x/y = k, k is any number that has a constant value. When two quantities are inverse proportions, x, and y, where x is increased, the value of y is decreased, represented as xy = k, k is any number. In a direct variation, as one number rises, the other rises as well. This is also known as direct proportion; the two terms are interchangeable. The connection between age and height is one example of this. As a child's age grows, so does his or her height. The equation y = kx can be used to represent direct variation in the abstract.The two values are x and y, which let, in our case, be the pressure and volume of a balloon. The constant of proportionality, k, informs you exactly how much larger y will become for every rise in x.

If y = 2x, for example, it indicates that for every rise in the volume, unit pressure will increase by twice as much. The larger the number you enter for x, the value of y would increase by the same factor to maintain the ratio of proportionality between them.

In an inverse variation, the reverse is true: as one number grows, the other decreases. This is sometimes referred to as inverse proportion. As an example, consider the link between time spent goofing around in class and your midterm grade. The more you blunder, the worse your exam score. If we were to give this one formula, we'd say: y = k/x, where x and y are the two values and k is the proportionality constant, indicating how much one varies when the other changes. In this equation, you can see that you divide a constant integer by x to get y. As a result, the larger the value of x, the lower the value of y. That is inverse variation: when one rises, the other falls.

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