Railneer is packaged in a water bottling plant, with die help of two machines and `M_1`. and `M_2`. `M_1` and `M_2` produces 400 and 600 bottles per minute. One day’s production can be processed by `M_1` operating alone for 9 hours, by `M_2` operating alone for 6 hours or by both and `M_1` and `M_2` operating simultaneously for 3 hours and 36 minutes. If one days production is processed by `M_1` operating alone for `1/3` of the time and `M_1` and `M_2` simultaneously operating for `2/3` of the time, then in how many hours total production of one day will be completed?

Options

A. 2
B. 3
C. 4.5
D. 4.8

Answer

To solve the problem step by step, we will first calculate the total production of one day and then determine how long it will take to complete that production given the conditions stated in the question.

### Step 1: Calculate Total Production in Bottles
1. **Calculate the total work done by M1 in one day:**
- M1 produces 400 bottles per minute.
- In 1 hour, M1 produces:
\[ 400 \text{ bottles/min} \times 60 \text{ min} = 24000 \text{ bottles/hour} \]
- In 9 hours, M1 produces:
\[ 24000 \text{ bottles/hour} \times 9 \text{ hours} = 216000 \text{ bottles} \]