Machines P, Q, R can each print 1,00,000 books in 8 h, 10 h, and 12 h respectively. All start at 9:00 A.M.; P stops at 11:00 A.M.; Q and R continue. Approximately when will all 1,00,000 books be printed?

Problem restatement
With staggered machine operation, compute total output over time to find the finishing clock time.

Given data

• P: 1,00,000 in 8 h → 12,500 books/hour.
• Q: 1,00,000 in 10 h → 10,000 books/hour.
• R: 1,00,000 in 12 h → 8,333.33 books/hour.
• P works only from 9:00 A.M. to 11:00 A.M. (2 hours).

Concept/Approach
Compute books printed by P before stopping, then finish the remainder with Q + R's combined rate. Convert hours to clock time.

Step-by-step calculation
Output by P in 2 h = 2 × 12,500 = 25,000 books Remaining = 1,00,000 − 25,000 = 75,000 books Combined rate (Q + R) = 10,000 + 8,333.33 ≈ 18,333.33 books/hour Time for remainder ≈ 75,000 ÷ 18,333.33 ≈ 4.0909 hours 0.0909 hours ≈ 0.0909 × 60 ≈ 5.45 minutes Finish time ≈ 11:00 A.M. + 4 h 6 min ≈ 3:06 P.M. (rounded ≈ 3:05 P.M.)

Verification/Alternative
Exact fractional rate: R = 100,000/12 = 25,000/3; Q + R = 10,000 + 25,000/3 = (30,000 + 25,000)/3 = 55,000/3 books/h. Time = 75,000 ÷ (55,000/3) = 75,000 × 3 / 55,000 = 225,000/55,000 ≈ 4.0909 h (same).

Common pitfalls

• Using average time instead of rate addition.
• Forgetting P contributes only for 2 hours.

Final Answer
Around 3:05 P.M.