A can do a work in 12 days and B can do a same work in 15 days. If both works together then how many days they will finished the total work?

Options

A. 6.66 days
B. 3.33 days
C. 8.33 days
D. 7.33 days

Answer

To solve the problem of how many days A and B will take to finish the work together, we can follow these steps:

### Step 1: Calculate the work done by A in one day.
A can complete the work in 12 days. Therefore, the work done by A in one day is:
\[ \text{Work done by A in one day} = \frac{1}{12} \]

### Step 2: Calculate the work done by B in one day.
B can complete the same work in 15 days. Therefore, the work done by B in one day is:
\[ \text{Work done by B in one day} = \frac{1}{15} \]

### Step 3: Calculate the total work done by A and B together in one day.
To find the total work done by A and B together in one day, we add the work done by A and B:
\[ \text{Total work done in one day} = \frac{1}{12} + \frac{1}{15} \]

### Step 4: Find a common denominator and add the fractions.
The least common multiple (LCM) of 12 and 15 is 60. We convert the fractions:
\[ \frac{1}{12} = \frac{5}{60} \quad \text{and} \quad \frac{1}{15} = \frac{4}{60} \]
Now, we can add them:
\[ \text{Total work done in one day} = \frac{5}{60} + \frac{4}{60} = \frac{9}{60} \]

### Step 5: Simplify the total work done in one day.
\[ \frac{9}{60} = \frac{3}{20} \]

### Step 6: Calculate the number of days to finish the work together.
If A and B together can do \(\frac{3}{20}\) of the work in one day, then the number of days required to complete the entire work is the reciprocal of this fraction:
\[ \text{Number of days} = \frac{1}{\frac{3}{20}} = \frac{20}{3} \approx 6.67 \text{ days} \]

### Final Answer:
A and B together will finish the work in \(\frac{20}{3}\) days, which is approximately 6.67 days.

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