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:

10 days

The correct answer is Option (2) → 10 days

Step 1: Let the rates of work per day

Let the work done per day by P, Q, R be p, q, r (fraction of job per day).

• P + Q together can do the job in 6 days → Work per day:

$p + q = \frac{1}{6}$​

• Q + R together can do the job in 60/7 days → Work per day:

$q + r = \frac{7}{60}$​

Step 2: Work done in sequence

• P worked 3 days:

$\text{Work by P} = 3p$

• Q and R continued for 6 days:

$\text{Work by Q + R} = 6(q+r) = 6 \cdot \frac{7}{60} = \frac{7}{10}$

Total work = 1, so:

$3p + \frac{7}{10} = 1$

$3p = 1 - \frac{7}{10} = \frac{3}{10}$

$p = \frac{1}{10}$

Step 3: Find Q and R's rates

• From Step 1: $p + q = \frac{1}{6}$​

$\frac{1}{10} + q = \frac{1}{6} ⇒q = \frac{1}{6} - \frac{1}{10} = \frac{5-3}{30} = \frac{2}{30} = \frac{1}{15}$

• From Step 1: $q + r = \frac{7}{60}$​

$\frac{1}{15} + r = \frac{7}{60} ⇒r = \frac{7}{60} - \frac{4}{60} = \frac{3}{60} = \frac{1}{20}$

Step 4: Days to complete job independently

• P alone: $1/p = 10$ days
• R alone: $1/r = 20$ days
• Difference = $20 - 10 = 10$ days

Correct answer: 10 days