A alone can do a work in 20 days. The ratio of time taken by ltbegt A and B to do the same work is 4:3 Then, find in how many
days both will complete the work together ?

Options

A. 7.25 days
B. 12 days
C. 8 days
D. 8.5 days

Explanation

To solve the problem, we will follow these steps:

### Step 1: Determine the work done by A in one day.
A can complete the work in 20 days. Therefore, the amount of work done by A in one day is:

\[ \text{Work done by A in one day} = \frac{1}{20} \]

### Step 2: Find the time taken by B to complete the work.
The ratio of the time taken by A and B is given as 4:3. Let the time taken by A be \(4x\) and the time taken by B be \(3x\). Since A takes 20 days to complete the work, we can set up the equation:

\[ 4x = 20 \implies x = 5 \]

Now, substituting \(x\) back to find the time taken by B:

\[ \text{Time taken by B} = 3x = 3 \times 5 = 15 \text{ days} \]

### Step 3: Determine the work done by B in one day.
Now, we can find the work done by B in one day:

\[ \text{Work done by B in one day} = \frac{1}{15} \]

### Step 4: Calculate the combined work done by A and B in one day.
To find the total work done by both A and B together in one day, we add their individual work rates:

\[ \text{Combined work done in one day} = \frac{1}{20} + \frac{1}{15} \]

To add these fractions, we need a common denominator. The least common multiple of 20 and 15 is 60. Thus, we convert the fractions:

\[ \frac{1}{20} = \frac{3}{60}, \quad \frac{1}{15} = \frac{4}{60} \]

Now, adding these:

\[ \text{Combined work done in one day} = \frac{3}{60} + \frac{4}{60} = \frac{7}{60} \]

### Step 5: Calculate the total time taken by A and B to complete the work together.
If A and B together can complete \(\frac{7}{60}\) of the work in one day, then the total time taken to complete 1 whole work is the reciprocal of this rate:

\[ \text{Total time taken} = \frac{1}{\frac{7}{60}} = \frac{60}{7} \text{ days} \]

### Final Answer:
Thus, A and B together will complete the work in \(\frac{60}{7}\) days, which is approximately 8.57 days.

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