If two quantities p and q vary inversely with each other then ______ of their corresponding values remain constant.
Solution:
The table below shows the relation between p and q as an inversely proportional.
|
p |
5/2 |
3/2 |
1/2 |
1/3 |
1/4 |
|
q |
2 |
10/3 |
10 |
15 |
20 |
From the table it is evident that as p decreases q is increasing. To verify that they have an inversely proportional relationship we have to find the product of p and q. It the product is a constant then it can be easily established that the relation between the two is inversely proportional
pq = 5/2 × 2 = 3/2 × 10/3 = 1/2 × 10 = 1/3 × 15 = 1/4 × 20 = 5
The product of p and q is constant and hence there exists an inversely proportional relationship between p and q.
✦ Try This: If two variables x and y are inversely proportional to each other then their product is a constant. Using this principle please complete the table below:
|
x |
2 |
3 |
4 |
5 |
|
|
y |
3 |
|
3/2 |
|
1 |
Given that the variables are inversely proportional to each other we can state that,
xy = constant
From the above table the following is evident:
xy = 2 × 3 = 4 × 3/2 = 6
Hence the blanks in the above table can be filled as shown below:
x = 3; xy = 6
Therefore y = 6/3 = 2
x = 5; xy = 6
Therefore y = 6/5
y = 1; xy = 6
x = 6/1 = 6
Hence the table can be completed as follows:
|
x |
2 |
3 |
4 |
5 |
6 |
|
y |
3 |
2 |
3/2 |
6/5 |
1 |
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 13
NCERT Exemplar Class 8 Maths Chapter 10 Problem 32
If two quantities p and q vary inversely with each other then ______ of their corresponding values remain constant.
Summary:
If two quantities p and q vary inversely with each other then product of their corresponding values remain constant.
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