This part contains two exercises that involve questions dependent on the direct proportion and inverse proportion. Two quantities x and y are supposed to be in direct proportion if they increment (decrease) together in a certain way that the ratio of their comparing values stays constant. Then again, two quantities x and y are supposed to be in inverse proportion if an expansion in x causes a proportional decrease in y (and the other way around) in such a way that the result of their relating values stays constant.
When two variables have changed in a similar sense, i.e., as one amount increases and at the same rate, the other amount simultaneously increases; it is called direct proportionality. When two variables such as x and y are given, y is directly proportional to x if there is non-zero constant k. The constant ratio is known as the constant of proportionality or proportionality constant.
If the value of a variable called x decreases or increases upon corresponding increase or decrease in the value of a variable called y, then we can say that variables x and y are in inverse proportion.
Time and Work
It is significant to establish the relationship between the time taken and the work is done in any given problem or situation. If time increases with an increase in work, then the relation is directly proportional.
If the value of a variable called x, always increases or decreases with the respective increase or decrease in value of a variable called y, then it is said that the variables x and y are in direct proportion.
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