Inverse Variation
Inverse Variation
If two quantities x and y vary with each other in such a manner that the product ab remains constant and is positive ,then we say that a and b vary inversely as each other or a varies inversely as b and b varies inversely as a. Thus, if two quantities a and b vary inversely as each other, then the product ab always remains constant .The product ab is called the constant of variation .
If two quantities a and b vary inversely to each other and if are the values of b corresponding to the values ,
of a respectively ,then
Rule: if two quantities a and b vary inversely as each other , then the ratio of any two values of a is equal to the inverse ratio of the corresponding values of b.
Illustration: If 52 men can do a piece of work in 35 days , in how many days 28 men will do it ?
Solution: Suppose 28 men will do the piece of the work in x days . The given information can be exhibited in the following tabular form.
| Number of men | 52 | 28 |
| Number of days | 35 | x |
Clearly, we can say that less is the number of men ,more will be the number of days required to finish the work.
It is therefore , the case of inverse variation .
Ratio of Number of men = Inverse ratio of number of days
Hence, 28 men will do the work in 65 days.
Illustration: Raghu has enough money to buy 75 machines worth Rs. 200 each. How many machines he can buy if he gets a discount of Rs. 50 on each machine?
Solution: Let x be the number of machines he can buy if he gets a discount of Rs. 50 on each machine.
This information can be formulated in the following table as follows
| Number of machines | 75 | x |
| Cost of machine(in Rupees) | 200 | 150 |
Amar takes 15 days to reduce 20 kilograms of his weight by doing 20 minutes of exercise per day. If he does exercise for 1 hour per day, how many days will he take to reduce the same weight? | |||
| Right Option : A | |||
| View Explanation | |||
The frequency of a vibrating guitar string varies inversely with its length. Suppose a guitar string 0.80 meters long vibrates 4 times per second. What frequency would a string 0.5 meters long have? | |||
| Right Option : A | |||
| View Explanation | |||
If a and b vary inversely, fill in the blanks:
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| Right Option : B | |||||||||||
| View Explanation | |||||||||||
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