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 two quantities x and y vary inversely with each other, then _______________________ | |||
| Right Option : D | |||
| View Explanation | |||
Students / Parents Reviews [10]
Abhyas is a complete education Institute. Here extreme care is taken by teacher with the help of regular exam. Extra classes also conducted by the institute, if the student is weak.
Om Umang
10thMy experience with Abhyas is very good. I have learnt many things here like vedic maths and reasoning also. Teachers here first take our doubts and then there are assignments to verify our weak points.
Shivam Rana
7thIt has a great methodology. Students here can get analysis to their test quickly.We can learn easily through PPTs and the testing methods are good. We know that where we have to practice
Barkha Arora
10thA marvelous experience with Abhyas. I am glad to share that my ward has achieved more than enough at the Ambala ABHYAS centre. Years have passed on and more and more he has gained. May the centre flourish and develop day by day by the grace of God.
Archit Segal
7thAbhyas Methodology is very good. It is based on according to student and each child manages accordingly to its properly. Methodology has improved the abilities of students to shine them in future.
Manish Kumar
10thMy experience was very good with Abhyas academy. I am studying here from 6th class and I am satisfied by its results in my life. I improved a lot here ahead of school syllabus.
Ayan Ghosh
8thOne of the best institutes to develope a child interest in studies.Provides SST and English knowledge also unlike other institutes. Teachers are co operative and friendly online tests andPPT develope practical knowledge also.
Aman Kumar Shrivastava
10thBeing a parent, I saw my daughter improvement in her studies by seeing a good result in all day to day compititive exam TMO, NSO, IEO etc and as well as studies. I have got a fruitful result from my daughter.
Prisha Gupta
8thIt was good as the experience because as we had come here we had been improved in a such envirnment created here.Extra is taught which is beneficial for future.
Eshan Arora
8thIt 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.
