MULTIPLYING RATIO
We can say that, problems related to both direct & inverse variation can be solved by finding what is known as the multiplying ratio.
For your better understanding we would like to give some example –
Example.1) If 8 kg of rice costs $ 320, find the cost of 15 kg of rice
Answer) Since the cost increases when the weight increases, this an example of Direct variation
So, the ratio of the weight = the ratio of the corresponding costs
8 $ 320
So, ------- = ---------, where $ x is the cost of 15 kg of rice
15 x
$ 320 X 15
So, x = -------------- = $ 600
8
15
Here --------- is the multiplying ratio.
8
If, two quantity changes in the same ratio, the multiplying ratio is the inverse of the ratio.
Another way –
As per the given condition, 8 kg of rice costs $ 320
$ 320
Then, 1 kg of rice costs
= ----------
8
[ here we divide total price ($ 320) by quantity (8 kg), because the cost of 1 kg rice will be less than 8 kg rice ]
15
Now, the cost of 15 kg rice will be = $ 320 X ---------
8
(here 15 / 8 is the multiplying ratio)
[ here we will multiply by the given quantity which is 15 kg with the cost of 1 kg rice ]
= $ 600 (Ans.)