A can do a piece of work in 10 days and B in 12 days. With help of C, they finish the work in 4 days. In how many days C along can do the same work?

Options

A. 12
B. 15
C. 18
D. 24

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Determine the work done by A and B
- A can complete the work in 10 days, so the work done by A in one day is:
\[ \text{Work done by A in 1 day} = \frac{1}{10} \text{ of the work} \]

- B can complete the work in 12 days, so the work done by B in one day is:
\[ \text{Work done by B in 1 day} = \frac{1}{12} \text{ of the work} \]

### Step 2: Calculate the combined work done by A and B in one day
- To find the total work done by A and B together in one day, we add their individual contributions:
\[ \text{Work done by A and B in 1 day} = \frac{1}{10} + \frac{1}{12} \]
- To add these fractions, we find a common denominator, which is 60:
\[ \frac{1}{10} = \frac{6}{60}, \quad \frac{1}{12} = \frac{5}{60} \]
- Therefore,
\[ \text{Work done by A and B in 1 day} = \frac{6}{60} + \frac{5}{60} = \frac{11}{60} \]

### Step 3: Calculate the total work done by A, B, and C in one day
- It is given that A, B, and C together finish the work in 4 days. Thus, the work done by A, B, and C together in one day is:
\[ \text{Work done by A, B, and C in 1 day} = \frac{1}{4} \]
- Converting this to a fraction with a denominator of 60:
\[ \frac{1}{4} = \frac{15}{60} \]

### Step 4: Determine the work done by C in one day
- Now, we can find the work done by C in one day by subtracting the work done by A and B from the total work done by A, B, and C:
\[ \text{Work done by C in 1 day} = \frac{15}{60} - \frac{11}{60} = \frac{4}{60} = \frac{1}{15} \]

### Step 5: Calculate the number of days C alone would take to finish the work
- If C can do \(\frac{1}{15}\) of the work in one day, then the number of days C alone would take to complete the entire work is:
\[ \text{Days taken by C} = \frac{1}{\frac{1}{15}} = 15 \text{ days} \]

### Final Answer
C alone can complete the work in **15 days**.

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