In a press, there are three types of printing machines, P, Q and R. Machine P can print 10,000 pages in 8 hours, machine Q can finish the same task in 10 hours and machine R can finish the same task in 15 hours. All the three machines start the work at `9 : 00` a. m. Machine P breaks down at `11 : 00` a.m. and machines Q and R finish the task. The approximate time of completion of the job is :

Options

A. `2:05` p.m.
B. `2:30` p.m.
C. `1:50` p.m.
D. `1:30` p.m.

Answer

To solve the problem step by step, we will first calculate the efficiency of each machine, then determine how much work is completed before machine P breaks down, and finally calculate the time taken by machines Q and R to finish the remaining work.

### Step 1: Calculate the efficiency of each machine
- Machine P can print 10,000 pages in 8 hours.
- Machine Q can print 10,000 pages in 10 hours.
- Machine R can print 10,000 pages in 15 hours.

**Efficiency Calculation:**
- Efficiency of P = Total Work / Time taken by P = 10,000 pages / 8 hours = 1,250 pages/hour
- Efficiency of Q = Total Work / Time taken by Q = 10,000 pages / 10 hours = 1,000 pages/hour
- Efficiency of R = Total Work / Time taken by R = 10,000 pages / 15 hours = 666.67 pages/hour

### Step 2: Calculate the total efficiency when all machines work together
- Total Efficiency = Efficiency of P + Efficiency of Q + Efficiency of R
- Total Efficiency = 1,250 + 1,000 + 666.67 = 2,916.67 pages/hour

### Step 3: Calculate the work done in the first 2 hours
- All machines work together from 9:00 AM to 11:00 AM (2 hours).
- Work done in 2 hours = Total Efficiency × Time = 2,916.67 pages/hour × 2 hours = 5,833.34 pages

### Step 4: Calculate the remaining work
- Total work = 10,000 pages
- Work done = 5,833.34 pages
- Remaining work = Total work - Work done = 10,000 - 5,833.34 = 4,166.66 pages

### Step 5: Calculate the combined efficiency of machines Q and R
- Combined Efficiency of Q and R = Efficiency of Q + Efficiency of R
- Combined Efficiency = 1,000 + 666.67 = 1,666.67 pages/hour

### Step 6: Calculate the time taken by Q and R to finish the remaining work
- Time = Remaining Work / Combined Efficiency
- Time = 4,166.66 pages / 1,666.67 pages/hour = 2.5 hours

### Step 7: Calculate the total time taken for completion
- Total time = Time worked by all machines + Time taken by Q and R
- Total time = 2 hours (from 9:00 AM to 11:00 AM) + 2.5 hours = 4.5 hours

### Step 8: Calculate the completion time
- Start time = 9:00 AM
- Total time = 4.5 hours
- Completion time = 9:00 AM + 4.5 hours = 1:30 PM

### Final Answer
The approximate time of completion of the job is **1:30 PM**.

---