Inverse Proportion
Two quantities may change in such a manner that if one quantity increases, the other quantity decreases. For example as the number of copies of xerox increases, the cost decreases. Similarly the number of workers increases, time taken to finish the job decreases.
Let us look into the following situation
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Sachin can go to his office in four different ways. He can walk, run, cycle or go by car. Study the following table
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Walking |
Running |
Cycling |
By car |
Speed (km/m) |
2 |
4 |
6 |
30 |
Time taken (in min) |
30 |
15 |
10 |
2 |
From the table as the speed increases, time taken to cover the distance decreases.
As Sachin doubles his speed by running, time reduces to half. As he increases his speed to 3 times by cycling, time decreases to one third. Similarly as he increases his speed to 15 times the time taken decreases to one fifteenth.
So from the above example if we increase the speed time taken decreases. It is a inverse proportion.
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5 tankers are required to fill a tank in 2 hours 30 minutes. How long will it take if only 3 tankers of the same type are used?
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Number of tankers |
5 |
3 |
Time (in minutes) |
150 |
x |
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Lesser the number of tankers, more will be time required by it to fill the tank. So this is a inverse proportion.
Time taken to fill the tank by 3 tanks is 4hrs 16 minutes.
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There are 30 students in a class. The number of table required for them is 18. If 15 of them are added to this class how many tables will be needed?
Number of students |
30 |
45 |
Number of tables |
18 |
? |
As the number of students increases number of tables required for the class also increases. This is a direct proportion.
Number of tables required = 27.
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If 10 workers clear the tank in 24 hours. How many workers will be required to do the same work same work in 12 hours.
Number of hours |
24 |
12 |
Number of workers |
10 |
x |
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As the time decreases, number of workers involved in that work increases. This is an inverse proportion.
20 workers are need to complete the same work in 12 hrs