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 |
If a and b vary inversely, fill in the blanks:
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| Right Option : B | |||||||||||
| View Explanation | |||||||||||
Students / Parents Reviews [20]
It was a good experience with Abhyas Academy. I even faced problems in starting but slowly and steadily overcomed. Especially reasoning classes helped me a lot.
Cheshta
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8thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
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