A can complete a work in 20 days and B can complete the same work in 25 days . If both of them work together, in 3 days what per cant of the total work will be completed ?

Options

A. 9
B. 12
C. 25
D. 27

Answer

To solve the problem step by step, we will first determine the work rates of A and B, then calculate how much work they complete together in 3 days, and finally convert that into a percentage of the total work.

### Step 1: Determine the work rates of A and B
- A can complete the work in 20 days. Therefore, A's work rate is:
\[ \text{Work rate of A} = \frac{1}{20} \text{ work per day} \]

- B can complete the work in 25 days. Therefore, B's work rate is:
\[ \text{Work rate of B} = \frac{1}{25} \text{ work per day} \]

### Step 2: Calculate the combined work rate of A and B
- When A and B work together, their combined work rate is:
\[ \text{Combined work rate} = \text{Work rate of A} + \text{Work rate of B} = \frac{1}{20} + \frac{1}{25} \]

- To add these fractions, we need a common denominator. The least common multiple of 20 and 25 is 100.
\[ \frac{1}{20} = \frac{5}{100}, \quad \frac{1}{25} = \frac{4}{100} \]
\[ \text{Combined work rate} = \frac{5}{100} + \frac{4}{100} = \frac{9}{100} \text{ work per day} \]

### Step 3: Calculate the total work done in 3 days
- In 3 days, the amount of work completed by A and B together is:
\[ \text{Work completed in 3 days} = \text{Combined work rate} \times 3 = \frac{9}{100} \times 3 = \frac{27}{100} \]

### Step 4: Convert the work done into a percentage of the total work
- To find the percentage of the total work completed, we multiply the fraction of work completed by 100:
\[ \text{Percentage of work completed} = \frac{27}{100} \times 100 = 27\% \]

### Final Answer
Thus, the percentage of the total work completed by A and B together in 3 days is **27%**.

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