Question

Two people could fit new windows in a house in 3 days.
(I) One of the persons fell ill before the work started. How long would the job take now?
(II) How many people would be needed to fit the windows in 1 day?

Answer 1

Hint – Find the relation between the number of people and the number of days taken.
Inverse proportion => ${{\text{x}}_1}{{\text{y}}_1} = {{\text{x}}_2}{{\text{y}}_2}$
If an increase in one quantity tends to the decrease in the other, it is called an inverse proportion.

Complete step by step answer:
(I) Given, 2 people can fix the windows in 3 days.
If one person fell in, then the other person must do the entire job.
We need to find how long this person takes.
Let the time taken be x days.
Therefore,
Number of persons 2 1
Time taken in days 3 x
As we increase the number of people, the time taken decreases.
They are in inverse proportion i.e.
2 × 3 = x × 1 (${{\text{x}}_1}{{\text{y}}_1} = {{\text{x}}_2}{{\text{y}}_2}$)
∴x= 6
Hence, 1 person will complete the job in 6 days.

(II) Now we need to find the number of people required to finish the work in 1 day.
Let the Number of people required be y.
Our table will look like
Number of persons 2 y
Time taken in days 3 1
As the number of people increases, the days decrease.
They are in inverse proportion i.e.
2 × 3 = y × 1
∴y = 6.
The number of people required to finish the work in 1 day is 6 people.

Note – In such problems it is important to identify if the variables given are either in direct proportion or indirect proportion and then apply the formula accordingly. The variables are in direct proportion if one decreases/ increases with the decrease/increase in the other respectively. The variables are in inverse proportion if one increases/decreases with the decrease/increase in the other respectively.