Pruthi and Shakil can complete a work in 20 days and 12 days respectively. Pruthi alone started the work and Shakil joined him after 4 days till the completion of the work. How long dd the work last?

Options

A. 5 days
B. 10 days
C. 14 days
D. 22 days

Answer

To solve the problem step by step, we will first determine the work done by Pruthi and Shakil individually, then calculate the work done during the time they worked together.

### Step 1: Determine the work rates of Pruthi and Shakil
- Pruthi can complete the work in 20 days, so his work rate is:
\[ \text{Pruthi's work rate} = \frac{1}{20} \text{ work/day} \]

- Shakil can complete the work in 12 days, so his work rate is:
\[ \text{Shakil's work rate} = \frac{1}{12} \text{ work/day} \]

### Step 2: Calculate the total work in terms of a common unit
To make calculations easier, we can assume the total work is 60 units (the least common multiple of 20 and 12).

- Therefore, Pruthi's efficiency in terms of work units is:
\[ \text{Pruthi's efficiency} = \frac{60}{20} = 3 \text{ units/day} \]

- And Shakil's efficiency is:
\[ \text{Shakil's efficiency} = \frac{60}{12} = 5 \text{ units/day} \]

### Step 3: Calculate the work done by Pruthi in the first 4 days
- In the first 4 days, Pruthi works alone:
\[ \text{Work done by Pruthi in 4 days} = 3 \text{ units/day} \times 4 \text{ days} = 12 \text{ units} \]

### Step 4: Calculate the remaining work
- The total work is 60 units, and Pruthi has completed 12 units. Therefore, the remaining work is:
\[ \text{Remaining work} = 60 - 12 = 48 \text{ units} \]

### Step 5: Calculate the combined work rate of Pruthi and Shakil
- When Shakil joins Pruthi, their combined work rate is:
\[ \text{Combined work rate} = 3 + 5 = 8 \text{ units/day} \]

### Step 6: Calculate the time taken to complete the remaining work
- To find the time (D) taken to complete the remaining 48 units of work together:
\[ D = \frac{\text{Remaining work}}{\text{Combined work rate}} = \frac{48 \text{ units}}{8 \text{ units/day}} = 6 \text{ days} \]

### Step 7: Calculate the total time taken to complete the work
- The total time taken to complete the work is the time Pruthi worked alone plus the time they worked together:
\[ \text{Total time} = 4 \text{ days} + 6 \text{ days} = 10 \text{ days} \]

Thus, the total duration of the work is **10 days**.

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