P and Q together can do a job in 6 days. Q and R can finish the same job in 60/7 days. P started the work and worked for 3 days. Q and R continued for 6 days and finish the work. Then, the difference of days in which R and P, independently can complete the job is:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 10 days
Each person’s one-day work is the fraction of the job done in a day, and the fractions done by everyone must add up to the whole job (1). The joint figures give P + Q and Q + R; the way the job was finished gives P alone, and the rest follows.
P and Q together: \(p+q=\frac{1}{6}\) of the job a day
Q and R together: the job in \(\frac{60}{7}\) days, so \(q+r=\frac{7}{60}\) a day
P worked 3 days, then Q and R worked 6 days and finished: \(3p+6\times\frac{7}{60}=1\)
P’s one-day work: \(3p=1-\frac{7}{10}=\frac{3}{10}\), so \(p=\frac{1}{10}\): P alone needs 10 days
Q’s one-day work, from P + Q: \(q=\frac{1}{6}-\frac{1}{10}=\frac{5-3}{30}=\frac{1}{15}\)
R’s one-day work, from Q + R: \(r=\frac{7}{60}-\frac{1}{15}=\frac{7-4}{60}=\frac{3}{60}=\frac{1}{20}\): R alone needs 20 days
Difference between R’s and P’s days \(=20-10=10\) days