Ranjith can complete a task in 25 days while Anji can finish it in 20 days .They work together on the task for 5 days and then Ranjith leaves in how many days Anji finish the remaining work ?

Options

A. 15 days
B. 10 days
C. 11 days
D. 9 days

Answer

To solve the problem, we need to determine how much work Ranjith and Anji can do together in 5 days, and then calculate how much work Anji can complete alone after Ranjith leaves.

### Step 1: Calculate the work done by Ranjith and Anji in one day.

- Ranjith can complete the task in 25 days. Therefore, his work rate (efficiency) is:
\[ \text{Ranjith's work rate} = \frac{1}{25} \text{ of the task per day} \]

- Anji can complete the task in 20 days. Therefore, her work rate is:
\[ \text{Anji's work rate} = \frac{1}{20} \text{ of the task per day} \]

### Step 2: Calculate their combined work rate.

- Together, their combined work rate is:
\[ \text{Combined work rate} = \text{Ranjith's work rate} + \text{Anji's work rate} = \frac{1}{25} + \frac{1}{20} \]

To add these fractions, we need a common denominator. The least common multiple of 25 and 20 is 100.

- Converting the fractions:
\[ \frac{1}{25} = \frac{4}{100} \quad \text{and} \quad \frac{1}{20} = \frac{5}{100} \]

- Now, adding them:
\[ \text{Combined work rate} = \frac{4}{100} + \frac{5}{100} = \frac{9}{100} \]

Thus, together they can complete \(\frac{9}{100}\) of the task in one day.

### Step 3: Calculate the work done in 5 days.

- In 5 days, the amount of work they complete together is:
\[ \text{Work done in 5 days} = 5 \times \frac{9}{100} = \frac{45}{100} = \frac{9}{20} \]

### Step 4: Calculate the remaining work.

- The total work is considered as 1 (the whole task). Therefore, the remaining work after 5 days is:
\[ \text{Remaining work} = 1 - \frac{9}{20} = \frac{20}{20} - \frac{9}{20} = \frac{11}{20} \]

### Step 5: Calculate how long it takes Anji to finish the remaining work.

- Anji's work rate is \(\frac{1}{20}\) of the task per day. To find out how many days it takes her to complete the remaining \(\frac{11}{20}\) of the task, we use the formula:
\[ \text{Time} = \frac{\text{Remaining work}}{\text{Anji's work rate}} = \frac{\frac{11}{20}}{\frac{1}{20}} = 11 \text{ days} \]

### Final Answer:
Anji will finish the remaining work in **11 days**.

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