# CLASS-8UNITARY METHOD-INVERSE VARIATION

INVERSE VARIATION

In Inverse Variation, the ratio of the two values of the first quantity (independent variable) is the inverse of the ratio of the two values of the second quantity (dependant variable). The multiplying ratio is the same as the ratio in which the first quantity changes. In the case of inverse proportion, the multiplying ratio is the same as the ratio in which the first variable ( or the independent variable ) changes.

It has been seen and concluded that, when Two quantities x & y are said to vary indirectly or be in Inverse Variation or in Inverse Proportion, if they change in such a way that the ratio of two values of x is the same as the inverse of the ratio of the corresponding two values of y, to put it more simply, when two quantities x & y are to be placed in inverse proportion, an increase in x (independent variable) causes a decrease in y (independent variable), while a decrease in x causes an increase in y.

For your better understanding, we would like to give you some example –

Example.) if 14 workers do a piece of work in 25 days, then 35 workers will do the work in 10 days. Provided they all work at the same rate. Here, the number of workers (x) changes in the ratio 14 : 35, i.e., 2 : 5 while the number of days (y) changes in the ratio  25 : 10, i.e., 5 : 2. So, the two quantities are in inverse variation. This is to be remembered that, more the number of workers less is the number of days. Similarly, less the number of workers, more will be the number of days. So, when x ( number of workers ) increases, y ( number of days ) decreases, and vice versa.

Another way –

As per the given condition -

If, 14 workers do a piece of work in 25 days

Then, 1 worker will do the same work in ( 25 X 14 ) days [ 1 worker will do or execute the total work in maximum days, so we will multiply total workers with total days ]

25 X 14

Now, 35 workers will do the same work in = --------------

35

(Inverse variation)

[ 35 workers will execute the same work by less/fewer days than the number of days will be taken to execute the same work by 1 worker, so we will divide by 35 workers ]                                                                                                    =   10 days

So, we can conclude that now 35 workers execute the same work by 10 days.    (Ans.)