Question

P and Q can finish the work in 10 days, while Q and R can finish the same work in 18 days. If P works for 5 days and Q works for 8 days, then remaining work is finished by R in 14 days. In how many days can R alone finish the work?

Answer 1

Answer: 33 days

Step-by-step explanation: Let us list what is given to us:

P+Q =  10 days

Q+R = 18 days

P works for 5 days

Q works for 8 days

R finishes the rest in 14 days

Therefore P+Q in 5 days = 1/2 of the work

Q+R in 3 days = 3/18 = 1/6th of the work

So total work done = 1/2+1/6=4/6 or 2/3rd of the work

So 1/3rd of the work is finished by R in (14-3) or 11 days

Therefore the whole work will be done in 11×3 days

=33 days

Hope this helps!