If P is thrice as good a workman as Q and finishes work 60 days less than Q, how many days does Q take to finish the work?

To understand why the number of days Q takes to finish the work is 90, we need to analyze the relationship between the work rates of P and Q.

If P is thrice as good a workman as Q, this implies that P can do three times the amount of work in the same amount of time compared to Q. Let's assume Q takes 'd' days to complete the work. Therefore, Q's work rate is 1/d (where 1 represents the whole job).

Since P is thrice as efficient, P's work rate will be 3/d, indicating P can complete the job in d/3 days.

According to the problem, P finishes the work 60 days less than Q. We can express this relationship mathematically:

[

d/3 = d - 60

]

To solve for d, we can first eliminate the fraction by multiplying the entire equation by 3:

[

d = 3(d - 60)

]

Expanding the right side gives:

[

d = 3d - 180

]

Rearranging the terms will yield:

[

180 = 3d - d

]

This simplifies to:

[

180 = 2d