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 :

Comments

Post a Comment

Popular posts from this blog

Series Order tricks, shortcuts and examples.

Image
Series Order tricks : A category of three, four or some numbers is given in the competitive examination. There is a mutual relationship among these numbers. The same relationship has to be understand and the same basis is to be increased further. Examples : 1) What will be the next number in the following series. 3, 10, 31, 94, ----- Ans. : Each terms is increasing by : ( n × 3 ) + 1. Therefore, ( 3 × 3 ) + 1 = 10 ( 10 × 3 ) + 1 = 31 ( 31 × 3 ) + 1 = 94 ( 94 × 3 ) + 1 = 283 Therefore, next number : 283. 2) Find the next order in the category. 1, 4, 9, 16, ---- Ans. : Each term is a squares of consecutive numbers. therefore, 5 × 5 = 25. therefore, next number = 25. Examples : Q. What will be the next number in the following series .  1) 3, 6, 10, 15, 21, ---- Ans. : The difference in each term is increasing in the form of consecutive numbers. that is 3 + 3 = 6. 06 + 4 = 10. 10 + 5 = 15. 15 + 6 = 21. 21 + 7 = 28. T...
Read more

Ratio and Proportion : formulas, tricks | proportion and ratio examples

Image
Ratio and Proportion : Ratio: In a cricket match, Sachin scored 160 runs and Rahul scored 80 runs. We can compare their scores in two ways : 1) By Subtraction : Sachin's score - Rahul's score = 160 - 80                                                  = 80 Thus, we see that Sachin has scored 80 runs more than Rahul. 2 ) By division : Let us see how many times Sachin's score is that of Rahul's. To do this, we shall divide Sachin's score by Rahul's. Sachin's score / Rahul's  score = 160 /  80 = 2 / 1. Thus, we see, that Sachin's score is 2 times Rahul's score. Definition of Ratio : "When two quantities are compared by division, then the quotient of that division is called a 'ratio'. The colon ':' is used to express a ratio." The ratio x/y is written as 'x:y' and is read as 'x  is to y'. In the ratio x : y , we call x as the first te...
Read more

Mode in statistics | How to calculate the mode | Mode formula.

Image
Mode in statistics : Mode definition : For example, some data such as follows : 2, 1, 2, 5, 4, 2, 2, 7, 8, 2. Here, 2 value repeated 5 times that is repeated many times as compared another data. Therefore, 2 is Mode." It is straight forward to calculate mode in case of individual and discrete data.               Mean          Median         Quartile How do you find the mode of  Individual Data ? Que. 1) The following are the marks of 10 students. Calculate the mode. 60, 67, 76, 56, 77, 67, 48, 67, 89, 90. Ans. : Marks            : 48  56  60  67  76  77  89  90 Frequency   :  01  01  01  03  01  01  01  01 Here 67 mark repeated many times that is 3 times. therefore, Mode = 67. Que. 2)  The following are the height in cm of 12 students. Calculate the mode. ...
Read more