"SANJAY Book Depot" can print one lakhs books in 8 hours. "DEVINDER & Sons" can print the same number of books in 10 hours while "HARISH & Sons" can print the same in 12 hours. All of them started printing at 0900 hrs. "SANJAY" is stopped at 1100 hrs and the remanining two machines complete the remaining leftover work. Approximately at what time will the printing of one lakhs books be completed?

Options

A. 1500 hrs
B. 1400 hrs
C. 1400 hrs
D. 1200 hrs

Answer

To solve the problem step by step, we need to calculate the work done by each printing press, the total work completed before Sanjay stops, and then determine how long it will take for Devinder & Sons and Harish & Sons to finish the remaining work.

### Step 1: Calculate the work rate of each printing press
1. **Sanjay Book Depot**:
- Time taken to print 1 lakh books = 8 hours
- Work rate = 1 lakh books / 8 hours = 12,500 books/hour

2. **Devinder & Sons**:
- Time taken to print 1 lakh books = 10 hours
- Work rate = 1 lakh books / 10 hours = 10,000 books/hour

3. **Harish & Sons**:
- Time taken to print 1 lakh books = 12 hours
- Work rate = 1 lakh books / 12 hours = 8,333 books/hour

### Step 2: Calculate the total work done by all three printing presses in 2 hours
- Work done in 1 hour by all three presses:
- Total work rate = 12,500 + 10,000 + 8,333 = 30,833 books/hour

- Work done in 2 hours:
- Total work done = 30,833 books/hour * 2 hours = 61,666 books

### Step 3: Calculate the remaining work after 2 hours
- Total work = 1 lakh books
- Remaining work = Total work - Work done
- Remaining work = 1,00,000 - 61,666 = 38,334 books

### Step 4: Calculate the combined work rate of Devinder & Sons and Harish & Sons
- Combined work rate of Devinder & Sons and Harish & Sons:
- Total work rate = 10,000 + 8,333 = 18,333 books/hour

### Step 5: Calculate the time taken to complete the remaining work
- Time taken to finish remaining work:
- Time = Remaining work / Combined work rate
- Time = 38,334 books / 18,333 books/hour ≈ 2.09 hours

### Step 6: Calculate the completion time
- Sanjay stops at 11:00 hours, and it takes approximately 2.09 hours to finish the remaining work.
- Completion time = 11:00 hours + 2.09 hours ≈ 13:05 hours (or approximately 1:05 PM)

### Final Answer
The printing of one lakh books will be completed approximately at **1:05 PM**.

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