Three cooks have to make 80 idlis. They are known to make 20 pieces every minute working together. The first cook began working alone and made 20 pieces having worked for sometime more than three minutes. The remaining part of the work was done by the second and the third cook working together. It took a total of 8 minutes to complete the 80 idlis. How many minutes would it take the first cook alone to cook 160 idlis for a marriage party the next day?

Options

A. 16 minutes
B. 24 minutes
C. 32 minutes
D. 40 minutes

Answer

To solve the problem step by step, let's break down the information provided and calculate accordingly.

### Step 1: Understand the total work and rates
- The three cooks together can make 20 idlis per minute.
- They need to make a total of 80 idlis.

### Step 2: Determine the time taken by the first cook
- The first cook worked alone and made 20 idlis.
- Since they make 20 idlis per minute together, the first cook must have taken a certain amount of time \( x \) to make those 20 idlis.
- We know that \( x \) must be slightly more than 3 minutes.

### Step 3: Calculate the time taken by the first cook
- The first cook's rate can be calculated as follows:
\[ \text{Time taken by first cook} = \frac{\text{Number of idlis made}}{\text{Rate of making idlis}} \]
Since the first cook made 20 idlis:
\[ x = \frac{20}{20} = 1 \text{ minute} \]
However, since the question states that he worked for more than 3 minutes, we need to adjust our understanding.

### Step 4: Calculate remaining work and time
- After the first cook made 20 idlis, there are \( 80 - 20 = 60 \) idlis left to be made.
- The total time taken to complete the work is 8 minutes. Therefore, the time taken by the second and third cooks together is:
\[ 8 - x \text{ minutes} \]

### Step 5: Determine the time taken by the second and third cooks
- The second and third cooks together make 20 idlis per minute. Thus, in \( 8 - x \) minutes, they can make:
\[ 20 \times (8 - x) \text{ idlis} \]
Setting this equal to the remaining 60 idlis:
\[ 20(8 - x) = 60 \]
Simplifying gives:
\[ 8 - x = 3 \implies x = 5 \text{ minutes} \]

### Step 6: Calculate the first cook's efficiency
- The first cook takes 5 minutes to make 20 idlis, so his rate is:
\[ \text{Rate of first cook} = \frac{20 \text{ idlis}}{5 \text{ minutes}} = 4 \text{ idlis per minute} \]

### Step 7: Calculate time for the first cook to make 160 idlis
- To find out how long it would take the first cook to make 160 idlis:
\[ \text{Time} = \frac{160 \text{ idlis}}{4 \text{ idlis per minute}} = 40 \text{ minutes} \]

### Final Answer
The first cook would take **40 minutes** to cook 160 idlis.