Question

1) If P and Q together can complete a job in 3 days while
P alone can do the same in 12 days, then how many days
would be required by Q to do the job alone?​

Answer 1

Step-by-step explanation:

Let P+Q, together, take x days to do the work.

P alone will do the same work in (x+12) days while Q does it in (x+3) days.

P does [1/(x+12)]th of the work in 1 day.

Q does [1/(x+3)]th of the work in 1 day.

So P and Q together do [1/(x+12)]+[1/(x+3)] or [x+3+x+12]/[(x+12)(x+3)] =(2x+15)/[(x+12)(x+3)]th part of the work in 1 day.

So P and Q will take [(x+12)(x+3)]/(2x+15) days which is the same as x.

Or, [(x+12)(x+3)]/(2x+15)=x, or

x^2+15x+36 = 2x^2+30, or

x^2–15x-6=0

x = [15+(225+24)^0.5]/2

= [15+15.78]/2

= 15.39

So P does the work, alone, in 27.39 days while Q, alone will do it in 18.39 days. Answer.