Question : P and Q together can do a job in 6 days. Q and R can finish the same job in $\frac{60}{7}$ days. P started the work and worked for 3 days. Q and R continued for 6 days. Then the difference in days in which R and P can complete the job is:
Option 1: 15
Option 2: 10
Option 3: 8
Option 4: 12
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Correct Answer: 10
Solution :
(P + Q)'s 1 day work = $\frac{1}{6}$
(Q + R)'s 1 day work = $\frac{7}{60}$
Let P alone take $x$ days to finish the work.
According to the question,
⇒ $\frac{3}{x}+\frac{6 \times 7}{60}=1$
⇒ $\frac{3}{x}=1-\frac{7}{10}$
⇒ $\frac{3}{x}=\frac{3}{10}$
⇒ $x=10$ days
Q's 1 day work = $\frac{1}{6}-\frac{1}{10}$
= $\frac{5-3}{30}$
= $\frac{1}{15}$
R's 1 day work = $\frac{7}{60}-\frac{1}{15}$
= $\frac{7-4}{60}$
= $\frac{1}{20}$
Time taken by R = 20 days
Difference of R and P = 20 – 10 = 10 days
Hence, the correct answer is 10.
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