P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave at the beginning for two days. R worked 18 hours a day on all days.

Question

P, Q, R and S are working on a project. Q can finish the task in 25 days, working alone for 12 hours a day. R can finish the task in 50 days, working alone for 12 hours per day. Q worked 12 hours a day but took sick leave at the beginning for two days. R worked 18 hours a day on all days. What is the ratio of work done by Q and R after 7 days from the start of the project?

Accepted Answer

20:21. Q's hourly work rate is $1/(25\times 12)$ of the job per hour, and R's hourly work rate is $1/(50\times 12)$. In 7 days, Q works for 5 days at 12 hours/day, while R works for 7 days at 18 hours/day. Comparing the total work gives the ratio $20:21$.

Solution

Related GATE General Aptitude questions