E and F can do a work in 10 days . If E alone can do it in 30 days . F alone can do it in___days.
A. 15
B.20
C. 25
D. 18.

Options

A. A
B. C
C. D
D. B

Answer

To solve the problem step by step, we will first determine the work done by E and F together, and then find out how long it takes for F to complete the work alone.

### Step 1: Determine the work done by E and F together
E and F can complete the work together in 10 days. This means that in one day, they can complete \( \frac{1}{10} \) of the work.

### Step 2: Determine the work done by E alone
E can complete the work alone in 30 days. This means that in one day, E can complete \( \frac{1}{30} \) of the work.

### Step 3: Set up the equation for work done by F
Let the work done by F in one day be represented as \( \frac{1}{F} \), where F is the number of days F takes to complete the work alone.

From the information given, we can write the equation:
\[ \text{Work done by E and F together} = \text{Work done by E} + \text{Work done by F} \]
This translates to:
\[ \frac{1}{10} = \frac{1}{30} + \frac{1}{F} \]

### Step 4: Solve for \( \frac{1}{F} \)
To isolate \( \frac{1}{F} \), we can rearrange the equation:
\[ \frac{1}{F} = \frac{1}{10} - \frac{1}{30} \]

### Step 5: Find a common denominator
The common denominator for 10 and 30 is 30. Thus, we can rewrite the fractions:
\[ \frac{1}{10} = \frac{3}{30} \]
So, we have:
\[ \frac{1}{F} = \frac{3}{30} - \frac{1}{30} = \frac{2}{30} \]

### Step 6: Simplify \( \frac{1}{F} \)
Now, simplify \( \frac{2}{30} \):
\[ \frac{1}{F} = \frac{1}{15} \]

### Step 7: Solve for F
Taking the reciprocal gives us:
\[ F = 15 \]

### Conclusion
F alone can complete the work in **15 days**. Thus, the answer is option A: 15.

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