Direct and Inverse Proportions

Direct Proportion

Direct proportion is the relationship between two variables whose ratio is equal to a constant value. In other words, direct proportion is a situation where an increase (or decrease) in one quantity causes a corresponding increase (or decrease) in the other quantity.

Mathematically, two quantities x and y are said to be in direct proportion if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

In other words, if (x / y) = m or x = my [m is a positive number], then x and y are said to vary directly. In such a case if y1, y2 are the values of y corresponding to the values x1, x2 of x respectively then (x1 / y1) = (x2 / y2). When two quantities x and y are in direct proportion (or vary directly) they are also written as x y.

Let’s take some real life examples of direct proportion.

(a) The cost of rice is directly proportional to the weight. This means that, if the quantity of rice increase (or decrease), the price will also increase (or decrease).

(b) Work done is directly proportional to the number of workers. This means that, more workers, more work and les workers, less work accomplished.

(c) The fuel consumption of a car is proportional to the distance covered. This means that, more workers, more work and les workers, less work accomplished.

Inverse Proportion

Inverse proportion is the relationship between two variables whose product is equal to a constant value. In other words, direct proportion is a situation where an increase (or decrease) in one quantity causes a corresponding decrease (or increase) in the other quantity.

Mathematically, 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.

In other words, if xy = m [m is a positive number], then x and y are said to vary inversely. In such a case if y1, y2 are the values of y corresponding to the values x1, x2 of x respectively then x1 y1 = x2 y2. When two quantities x and y are in inverse proportion (or vary inversely) they are also written as x ∞ (1 / y).

Let’s take some real life examples of inverse proportion.

(a) As the number of workers increases, time taken to finish the job decreases.

(b) If we increase the speed of a vehicle, the time taken to cover a given distance decreases.

(c) Cost of a book and number of books purchased in a fixed amount are inversely proportional.

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