If A can complete a work in 80 min and B can complete the same work in 40 min. Then in how much time A and B together can complete the work.

Options

A. A)26 min 20 seconds
B. B)26 min 40 seconds
C. C)25 min 40 seconds
D. D)28 min 40 seconds

Answer

To solve the problem of how long A and B together can complete the work, we can follow these steps:

### Step 1: Determine the work rates of A and B
- A can complete the work in 80 minutes. Therefore, A's work rate is:
\[ \text{Work rate of A} = \frac{1 \text{ work}}{80 \text{ minutes}} = \frac{1}{80} \text{ work/minute} \]
- B can complete the work in 40 minutes. Therefore, B's work rate is:
\[ \text{Work rate of B} = \frac{1 \text{ work}}{40 \text{ minutes}} = \frac{1}{40} \text{ work/minute} \]

### Step 2: Combine the work rates of A and B
- When A and B work together, their combined work rate is the sum of their individual work rates:
\[ \text{Combined work rate} = \frac{1}{80} + \frac{1}{40} \]

### Step 3: Find a common denominator and add the work rates
- The common denominator for 80 and 40 is 80. We can rewrite the second term:
\[ \frac{1}{40} = \frac{2}{80} \]
- Now, add the two rates:
\[ \text{Combined work rate} = \frac{1}{80} + \frac{2}{80} = \frac{3}{80} \text{ work/minute} \]

### Step 4: Calculate the time taken to complete the work together
- To find the time taken to complete 1 work unit together, we take the reciprocal of the combined work rate:
\[ \text{Time} = \frac{1 \text{ work}}{\frac{3}{80} \text{ work/minute}} = \frac{80}{3} \text{ minutes} \]

### Step 5: Convert the time into minutes and seconds
- Now, we convert \(\frac{80}{3}\) minutes into minutes and seconds:
\[ \frac{80}{3} = 26 \text{ minutes} + \frac{2}{3} \text{ minutes} \]
- To convert \(\frac{2}{3}\) minutes into seconds:
\[ \frac{2}{3} \times 60 = 40 \text{ seconds} \]
- Therefore, the total time taken by A and B together is:
\[ 26 \text{ minutes and } 40 \text{ seconds} \]

### Final Answer
A and B together can complete the work in **26 minutes and 40 seconds**.

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