Nirmit can do `2/3` rd of a job in 18 days. Kashish is twice as efficient as Nirmit. In how many days will kashish complete the job ?

Options

A. `29/4`
B. `27/2`
C. `31/2`
D. `13/2`

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine Nirmit's Work Rate
Nirmit can complete \( \frac{2}{3} \) of the job in 18 days.

To find out how long it takes Nirmit to complete the entire job, we can set up the equation:
\[ \text{Time to complete the whole job} = \frac{\text{Time taken for } \frac{2}{3} \text{ of the job}}{\frac{2}{3}} = 18 \text{ days} \times \frac{3}{2} \]
Calculating this gives:
\[ \text{Time to complete the whole job} = 18 \times \frac{3}{2} = 27 \text{ days} \]

### Step 2: Determine Kashish's Efficiency
Kashish is twice as efficient as Nirmit. If we denote Nirmit's efficiency as \( E \), then Kashish's efficiency will be \( 2E \).

### Step 3: Calculate Time Taken by Kashish
Since efficiency and time taken are inversely related, we can express the time taken by Kashish in terms of Nirmit's time:
\[ \text{Time taken by Kashish} = \frac{\text{Time taken by Nirmit}}{\text{Efficiency ratio}} = \frac{27 \text{ days}}{2} \]
Calculating this gives:
\[ \text{Time taken by Kashish} = \frac{27}{2} = 13.5 \text{ days} \]

### Conclusion
Kashish will complete the job in \( 13.5 \) days.

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