Question

P and Q can do piece of work in 18 days, Q and R can do it in 24 days, R and P can do it in 20 days. How much time will R take to finish the job?​

Answer 1

Answer:

720/13 days (Nearly 55 days)

Step-by-step explanation:

Information needed to find the time R will finish the job in = Total days required by P, Q, and R to finish the job.

P = Work done in 1 day by P

Q = Work done in 1 day by Q

R = Work done in 1 day by R

(P+Q)+(Q+R)+(R+P) = 2 * Work done in 1 day by P, Q and R

=> {(P+Q)+(Q+R)+(R+P)}/2 = Work done in 1 day by P, Q and R

=> (1/18+1/24+1/20)*1/2 = Work done in 1 day by P, Q and R

=> {(20 + 15 + 18 ) / 360} * 1/2 = Work done in 1 day by P, Q and R (L.C.M of 18, 24, 20 = 360)

=> (53/360)*1/2 = Work done in 1 day by P, Q and R

=> 53/720 = Work done in 1 day by P, Q and R

So,

if we know that work done in 1 day by P and Q = 1/18

And work done in 1 day by P, Q, and R = 53/720

Then, we can just subtract work done in 1 day by P, Q, and R by work done in 1 day by P and Q, i.e., 53/720 - 1/18 = (53 - 40)/720 = 13/720

So, Work done in 1 day by R = 13/720

∴ Days required by R to do that work = 720/13