P and Q can do a piece of work in 20 days and 30 days, respectively. They work together for 6 days, and then Q is replaced by R.…

Question

P and Q can do a piece of work in 20 days and 30 days, respectively. They work together for 6 days, and then Q is replaced by R. If the rest of the work is completed by P and R in 8 more days, in how many days can R alone complete 60% of the work?

1. A. 28 days
2. B. 48 days (Correct answer)
3. C. 34 days
4. D. 64 days

Correct Answer

Option B — 48 days

Detailed Solution & Explanation

The correct answer is 48 days.

Key Points

• Work done by P and Q together in 6 days:
  • 6 × (1/20 + 1/30) = 6 × (3 + 2)/60 = 6 × 1/12 = 1/2 of the job
• The remaining 1/2 is finished by P and R in 8 days:
  • 8 × (1/20 + 1/R) = 1/2
  • 8/20 + 8/R = 1/2 → 2/5 + 8/R = 1/2 → 8/R = 1/10
  • so R = 80 days for the whole job
• The question asks for 60% of the work: 0.6 × 80 = 48 days.

Additional Information

• Read the final line carefully — the answer is not R's time for the full job (80 days) but for 60% of it. That partial-work twist is the entire difficulty.
• Using an LCM of 60 units for the job gives the same result with whole numbers: P = 3 units/day, Q = 2, and R works out to 0.75 units/day, so 60 units take 80 days.
• Rates add, times do not — the commonest error in this topic is averaging the days.
• Where someone is *replaced* mid-task, split the work at that moment and treat the two stretches separately, exactly as here.