# Inverse Variation

Definition:

we can say two quantities are said to be in inverse variation if one quantity increases,then the other quantity decreases or when one quantdity decreases,the other quantity increases.

Where we use this method:

For example 12 men can do a work in 10 days.8 men can do the same work in 15 days. 16 men can do the same work in 7 days.This example shows that more men take less days and less men and number of days are in this variation.

Example 1:

10 workers can build a wall in 12 days.How many days will 15 workers take to build the same wall?

Solution:

Number of workers                      Number of days

10                                       12

15                                       n

Working rule: Here the number of  workers and days is i inverse variation. Because if the number of workers got increased then the number of days taken by the workers  to finish the work will become reduced.So it comes under this topic.To proceed this problem we have to multiply straight. But in direct variation we have to do cross multiply .

10 x 12   =   15 x n

n   =   (10 x 12)/15

n   =   8

There fore the number of days required to finish the work is 8 days.

Example 2:

In an army camp provisions were there for 500 men for 28 days. If 400 men attended the camp,then how long did the provisions last?

Solution:

Number of Men                          Number of days

500                                     28

400                                      n

Working rule: Here we have two parts number of men and number of days.If the number of men will be increased in this the provisions will be enough for only less number of days.So it comes under this topic.So we have to multiply straight.

500 x 28   =  400 x n

n   = (500 x 28) / 400

n  =  35 days

There fore the number of days the provisions lasted for 400 men = 35 days.

Inverse variation to Basic math 