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 | |||
40 labourers can build a house in 40 days. How many labourers should be engaged by the contractor to complete the work in 50 days? | |||
| Right Option : C | |||
| View Explanation | |||
If 12 women can weave 15 metres of cloth in a day, how many metres of cloth can be woven by 20 women in a day? | |||
| Right Option : C | |||
| View Explanation | |||
Students / Parents Reviews [20]
About Abhyas metholodology the teachers are very nice and hardworking toward students.The Centre Head Mrs Anu Sethi is also a brilliant teacher.Abhyas has taught me how to overcome problems and has always taken my doubts and suppoeted me.
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8thIn terms of methodology I want to say that institute provides expert guidence and results oriented monitering supplements by requsite study material along with regular tests which help the students to improve their education skills.The techniques of providing education helps the students to asses...
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