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: Calculate the total work done by all three in one day.
To find the total work done by Sita, Gita, and Meera together in one day, we add their individual contributions:
\[ \text{Total work done in one day} = \frac{1}{15} + \frac{1}{25} + \frac{1}{30} \]

### 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 we can add these fractions:
\[ \text{Total work done in one day} = \frac{10}{150} + \frac{6}{150} + \frac{5}{150} = \frac{21}{150} \]

### Step 4: Calculate the time taken to complete the work together.
If they complete \(\frac{21}{150}\) of the work in one day, the time taken to complete the entire work (1 unit of work) can be calculated by taking the reciprocal of the total work done in one day:
\[ \text{Time taken} = \frac{1}{\frac{21}{150}} = \frac{150}{21} = \frac{50}{7} \text{ days} \]

### Final Answer:
Thus, Sita, Gita, and Meera will take \(\frac{50}{7}\) days to complete the work together.

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