A works 3 times as fast as B. If B can complete a work in 60 days, then in how many days can A and B together complete the same work ?

Options

A. 20
B. 12
C. 15
D. 30

Explanation

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

### Step 1: Determine the time taken by A to complete the work.
Since A works 3 times as fast as B, if B takes 60 days to complete the work, then A will take:
\[ \text{Time taken by A} = \frac{60}{3} = 20 \text{ days} \]

### Step 2: Calculate the work done by A and B in one day.
- Work done by A in one day:
\[ \text{Work done by A in one day} = \frac{1}{20} \text{ of the work} \]
- Work done by B in one day:
\[ \text{Work done by B in one day} = \frac{1}{60} \text{ of the work} \]

### 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:
\[ \text{Total work done in one day} = \frac{1}{20} + \frac{1}{60} \]

To add these fractions, we need a common denominator. The least common multiple of 20 and 60 is 60. Thus, we can rewrite the fractions:
\[ \frac{1}{20} = \frac{3}{60} \]
So,
\[ \text{Total work done in one day} = \frac{3}{60} + \frac{1}{60} = \frac{4}{60} = \frac{1}{15} \]

### Step 4: Calculate the total time taken by A and B together to complete the work.
If A and B together complete \(\frac{1}{15}\) of the work in one day, then the total time taken to complete the entire work is:
\[ \text{Total time} = \frac{1}{\frac{1}{15}} = 15 \text{ days} \]

### Final Answer:
A and B together can complete the work in **15 days**.

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