A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
🕒 Time Calculation 🕒
Machine P’s work rate = 1 lakh books / 8 hours = 12,500 books/hour
Machine Q’s work rate = 1 lakh books / 10 hours = 10,000 books/hour
Machine R’s work rate = 1 lakh books / 12 hours = 8,333.33 books/hour
All machines work together from 9 A.M. to 11 A.M. (2 hours).
Work done by P in 2 hours = 12,500 books/hour × 2 hours = 25,000 books
Work done by Q in 2 hours = 10,000 books/hour × 2 hours = 20,000 books
Work done by R in 2 hours = 8,333.33 books/hour × 2 hours = 16,666.67 books
Total work done in 2 hours = 25,000 + 20,000 + 16,666.67 = 61,666.67 books
Remaining work = 1 lakh books – 61,666.67 books = 38,333.33 books
Now, only Q and R are working.
Combined work rate of Q and R = 10,000 books/hour + 8,333.33 books/hour
= 18,333.33 books/hour
Time taken to complete the remaining work = Remaining work / Combined work rate
= 38,333.33 books / 18,333.33 books/hour
= 2.09 hours (approximately)
Since P stopped working at 11 A.M., add the remaining time to 11 A.M.:
11 A.M. + 2 hours 6 minutes ≈ 1:06 P.M.
🎉 The work will be finished approximately at 1:06 P.M. 🕒
