P and Q together complete the job in 24 days.
P alone completes the job in 32 days.
P's work rate =321 of the job per day
P and Q together work rate =241 of the job per day
Q's work rate =241−321
Finding the common denominator (LCM of 24 and 32 is 96):
241=964
321=963
Q's work rate =964−963
Q's work rate =961 of the job per day
They worked together for 8 days.
Work completed =8×241
Work completed =248
Work completed =31 of the job
Remaining work =1−31
Remaining work =32 of the job
Days for Q to complete remaining work =32÷961
Days =32×96
Days =3192
Days =64
Therefore, Q will take 64 days to complete the remaining job.