A company has a job to prepare certain no. of cans and there are three machines A, B & C for this job. A can complete the job in 3 days, B can complete the job in 4 days and C can complete the job in 6 days. How many days the company will take to complete job if all the machines are used simultaneously?
A)4 days
B)4/3 days
C)3 days
D)12 days

Options

A. 4 days
B. 4/3 days
C. 3 days
D. 12 days

Answer

To solve the problem of how many days it will take for machines A, B, and C to complete the job when used simultaneously, we can follow these steps:

### Step 1: Determine the work done by each machine in one day.
- Machine A can complete the job in 3 days, so in one day, it completes \( \frac{1}{3} \) of the job.
- Machine B can complete the job in 4 days, so in one day, it completes \( \frac{1}{4} \) of the job.
- Machine C can complete the job in 6 days, so in one day, it completes \( \frac{1}{6} \) of the job.

### Step 2: Calculate the total work done by all machines in one day.
To find the total work done by all three machines in one day, we add their individual contributions:
\[ \text{Total work in one day} = \frac{1}{3} + \frac{1}{4} + \frac{1}{6} \]

### Step 3: Find a common denominator to add the fractions.
The least common multiple (LCM) of 3, 4, and 6 is 12. We will convert each fraction to have a denominator of 12:
- \( \frac{1}{3} = \frac{4}{12} \)
- \( \frac{1}{4} = \frac{3}{12} \)
- \( \frac{1}{6} = \frac{2}{12} \)

Now we can add them:
\[ \text{Total work in one day} = \frac{4}{12} + \frac{3}{12} + \frac{2}{12} = \frac{9}{12} = \frac{3}{4} \]

### Step 4: Calculate the total time taken to complete the job.
If all machines together complete \( \frac{3}{4} \) of the job in one day, we can find out how many days it will take to complete the whole job (1 job):
\[ \text{Time taken} = \frac{1 \text{ job}}{\frac{3}{4} \text{ job/day}} = \frac{4}{3} \text{ days} \]

### Final Answer:
The company will take \( \frac{4}{3} \) days to complete the job if all machines are used simultaneously.