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Question
Complete the following table showing an instance of inverse proportion. The table shows the number of workers carrying out a task and the number of days they take to do it.
Number of workers
30
20
10
Days
4
6
8
24
| Number of workers | 30 | 20 | 10 | ||
| Days | 4 | 6 | 8 | 24 |
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Solution
The number of workers and days have an inverse variation.
So, product of one set of values should be equal to the product of another set.
Finding sequentially all the missing values, let the missing values be x, y and z respectively.
30 : 4 and x : 8 follow inverse proportion rule.
∴ 30 × 4 = x × 8
⇒x = 15
30 : 4 and 10 : y follow inverse proportion rule.
∴ 30 × 4 = 10 × y
⇒y = 12
30 : 4 and z : 24 follow inverse proportion rule.
∴ 30 × 4 = z × 24
⇒z = 5
So ,the missing values can be arranged in the table as:
Number of workers
30
20
15
10
5
Days
4
6
8
12
24
So, product of one set of values should be equal to the product of another set.
Finding sequentially all the missing values, let the missing values be x, y and z respectively.
30 : 4 and x : 8 follow inverse proportion rule.
∴ 30 × 4 = x × 8
⇒x = 15
30 : 4 and 10 : y follow inverse proportion rule.
∴ 30 × 4 = 10 × y
⇒y = 12
30 : 4 and z : 24 follow inverse proportion rule.
∴ 30 × 4 = z × 24
⇒z = 5
So ,the missing values can be arranged in the table as:
| Number of workers | 30 | 20 | 15 | 10 | 5 |
| Days | 4 | 6 | 8 | 12 | 24 |
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