Variation : Introduction, Types of variation : Direct variation | Inverse variation.

Variation Introduction:
Variation Introduction
Types of Variation :
There are two types of variation such as follows :
1) Direct Variation
2) Inverse Variation.

Examples of Direct Variation :
1) If 10 books cost Rs. 100, then what is the cost of 15 such books ?
Ans. :
Here, as the cost of book will increases with an increases in their number, we have a case of direct variation.
x = Number of books = 10
y = Cost of 10 books = 100
therefore, x / y = 10 / 100
also,
Number of books = 15
Suppose cost of 15 books = Rs. y
In direct variation, the ratio of the number of books of the cost of books must be constant.
therefore,
10 / 100 = 15 / y
y = ( 100 × 15 ) / 10
y = 150
therefore, the cost of 15 books is Rs. 150

2) If the shadow of a 12 meter high building falls 9 meters then how many meters will the shadow of a 9 meter high building fall?
Ans. :
Suppose x = building height
y = building of shadow
x / y = 12 / 9 = 9 / y
therefore, y = ( 9 × 9 ) / 12
y = 81 / 12
y = 6.75 meters
Therefore, shadow of a 9 meter high building falls 6.75 meters

3) It takes 15 seconds to fill 2 buckets with one tap, how many buckets will be filled in half an hour?
Ans. :
Suppose x = buckets
and y = seconds
now, half an hour = 30 minute's = 30 × 60 = 1800 seconds.
x / y = 2 / 15 = x / 1800
therefore, x = (  2 × 1800 ) / 15
x = 240
Therefore, 240 buckets  filled in half an hour.

Examples of Inverse Variation :
1) A motorcar travelling at a speed of 60 km per hour takes 4 hours to travel from one town to another. how many hours would a car travelling at a speed of 40 km per hour take for the same journey?
Ans. :
Here, if the car's speed decreases the time for the journey increases.
therefore, this is an example of Inverse Variation.
Distance travelled in 1 hr. = 60 km.
Time taken = 4 hrs.
Distance travelled in 1 hr. = 40 km.
Time taken = y hr
This being an example of Inverse Variation, the product of the speed of the vehicle and  time taken for a journey will remain constant.
therefore, 60 × 4 = 40 × y
that is, 40y = 60 × 4
y = ( 60 × 4 ) / 40
y = 6
therefore, the journey will take 6 hours if the car travels at a speed of 40 km per hour.

9. Single equation method :

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