Rakesh and Siva can do a piece of work in 15 days and 18 days respectively. They work together for 5 days and then Rakesh leaves. In how many days will Siva alone finish the remaining work?

Options

A. 5
B. 6
C. 8
D. 7

Explanation

To solve the problem step by step, let's follow the logic presented in the video transcript.

### Step 1: Determine the total work
We will assume the total work to be 90 units. This is chosen because it is a common multiple of the days Rakesh and Siva take to complete the work (15 and 18 days).

### Step 2: Calculate Rakesh's work rate
Rakesh can complete the work in 15 days. Therefore, his work rate (units of work per day) is:
\[ \text{Rakesh's work rate} = \frac{90 \text{ units}}{15 \text{ days}} = 6 \text{ units/day} \]

### Step 3: Calculate Siva's work rate
Siva can complete the work in 18 days. Therefore, his work rate is:
\[ \text{Siva's work rate} = \frac{90 \text{ units}}{18 \text{ days}} = 5 \text{ units/day} \]

### Step 4: Calculate the work done by Rakesh and Siva together in 5 days
When Rakesh and Siva work together for 5 days, the total work done is:
\[ \text{Work done in 5 days} = (Rakesh's work rate + Siva's work rate) \times 5 \text{ days} \]
\[ = (6 + 5) \times 5 = 11 \times 5 = 55 \text{ units} \]

### Step 5: Calculate the remaining work
The remaining work after 5 days is:
\[ \text{Remaining work} = \text{Total work} - \text{Work done in 5 days} \]
\[ = 90 - 55 = 35 \text{ units} \]

### Step 6: Determine how long Siva will take to finish the remaining work alone
Siva's work rate is 5 units/day. To find out how many days (let's call it \(X\)) Siva will take to finish the remaining work, we set up the equation:
\[ \text{Remaining work} = Siva's work rate \times X \]
\[ 35 = 5 \times X \]
Now, solving for \(X\):
\[ X = \frac{35}{5} = 7 \text{ days} \]

### Conclusion
Siva will finish the remaining work alone in **7 days**.

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