Amrit is twice as good a painter as Kushal and together they finish a piece of work in 6 days. In how many days will Kushal alone finish the work ?

Options

A. 10
B. 12
C. 24
D. 18

Answer

To solve the problem, we will first define the efficiencies of Amrit and Kushal, and then use their combined work rate to find out how long Kushal would take to complete the work alone.

### Step 1: Define the efficiencies
Let the efficiency of Kushal be \( K \) (units of work per day). Since Amrit is twice as good a painter as Kushal, Amrit's efficiency will be \( 2K \).

### Step 2: Calculate their combined efficiency
When Amrit and Kushal work together, their combined efficiency is:
\[ K + 2K = 3K \]

### Step 3: Use the combined efficiency to find total work
According to the problem, together they finish the work in 6 days. Therefore, the total work can be expressed as:
\[ \text{Total Work} = \text{Combined Efficiency} \times \text{Time} = 3K \times 6 = 18K \]

### Step 4: Determine how long Kushal would take to finish the work alone
Since Kushal's efficiency is \( K \), the time taken by Kushal to finish the total work of \( 18K \) is given by:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Kushal's Efficiency}} = \frac{18K}{K} = 18 \text{ days} \]

### Conclusion
Kushal alone will finish the work in **18 days**.

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