Sita can do a work in 15 days and Gita can do it in 25 days and Meera in 30 days. How long will they take to do the work, if they work together?

Options

A. 7 days
B. 6 days
C. 7/50 days
D. None of these

Answer

To solve the problem of how long Sita, Gita, and Meera will take to complete the work together, we can follow these steps:

### Step 1: Determine the work done by each person in one day.
- Sita can complete the work in 15 days, so the work done by Sita in one day is:
\[ \text{Work done by Sita in one day} = \frac{1}{15} \]

- Gita can complete the work in 25 days, so the work done by Gita in one day is:
\[ \text{Work done by Gita in one day} = \frac{1}{25} \]

- Meera can complete the work in 30 days, so the work done by Meera in one day is:
\[ \text{Work done by Meera in one day} = \frac{1}{30} \]

### Step 2: Add the work done by all three in one day.
Now, we will add the work done by Sita, Gita, and Meera together:
\[ \text{Total work done in one day} = \frac{1}{15} + \frac{1}{25} + \frac{1}{30} \]

### Step 3: Find a common denominator to add the fractions.
The least common multiple (LCM) of 15, 25, and 30 is 150. We will convert each fraction to have a denominator of 150:
- For Sita:
\[ \frac{1}{15} = \frac{10}{150} \]
- For Gita:
\[ \frac{1}{25} = \frac{6}{150} \]
- For Meera:
\[ \frac{1}{30} = \frac{5}{150} \]

Now, adding these fractions:
\[ \text{Total work done in one day} = \frac{10}{150} + \frac{6}{150} + \frac{5}{150} = \frac{21}{150} \]

### Step 4: Simplify the total work done in one day.
We can simplify \(\frac{21}{150}\):
\[ \frac{21}{150} = \frac{7}{50} \]

### Step 5: Calculate the time taken to complete the work.
If they complete \(\frac{7}{50}\) of the work in one day, the total time taken to complete the entire work (1 unit of work) can be calculated as:
\[ \text{Time taken} = \frac{1}{\frac{7}{50}} = \frac{50}{7} \text{ days} \]

Thus, the time taken by Sita, Gita, and Meera to complete the work together is \(\frac{50}{7}\) days.

### Final Answer:
\[ \text{The time taken to complete the work together is } \frac{50}{7} \text{ days.} \]

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