Some-time after the new workers were introduced, all of the newly introduced workers left the work due to heavy rain and the efficiency of the remaining workers reduced by `20%` due to which the work finally got completed by delay of `60%` of the scheduled time then how much work still remained incomplete by the end of the scheduled time?

Options

A. `17 3/5%`
B. `21%`
C. `27 5/7%`
D. `28%`

Answer

To solve the problem step by step, we will analyze the situation and calculate the amount of work that remains incomplete by the end of the scheduled time.

### Step 1: Define Variables
Let:
- \( M \) = number of original workers
- \( X \) = number of newly introduced workers
- \( T \) = scheduled time to complete the work

### Step 2: Calculate Total Work
The total work done by all workers together in scheduled time \( T \) is:
\[ \text{Total Work} = (M + X) \times T \]

### Step 3: Calculate Efficiency After New Workers Leave
After the new workers leave, the efficiency of the remaining workers reduces by 20%. Therefore, the efficiency of the remaining workers becomes:
\[ \text{Remaining Efficiency} = 80\% \text{ of } (M + X) = 0.8(M + X) \]

### Step 4: Calculate Delayed Time
The work is completed with a delay of 60% of the scheduled time. Therefore, the actual time taken to complete the work is:
\[ \text{Actual Time} = T + 0.6T = 1.6T \]

### Step 5: Calculate Work Done in Actual Time
The work done by the remaining workers in the actual time is:
\[ \text{Work Done} = \text{Remaining Efficiency} \times \text{Actual Time} = 0.8(M + X) \times 1.6T = 1.28(M + X)T \]

### Step 6: Set Up the Equation
Now, we can set up the equation based on the total work and the work done:
\[ 1.28(M + X)T = (M + X)T \]
This indicates that the total work done in the actual time is less than the total work required.

### Step 7: Calculate Work Remaining
The remaining work can be calculated as:
\[ \text{Remaining Work} = \text{Total Work} - \text{Work Done} = (M + X)T - 1.28(M + X)T \]
\[ = (1 - 1.28)(M + X)T = -0.28(M + X)T \]

### Step 8: Calculate Percentage of Incomplete Work
To find out how much work remains incomplete by the end of the scheduled time, we can express this as a percentage of the total work:
\[ \text{Percentage of Incomplete Work} = \left(\frac{-0.28(M + X)T}{(M + X)T}\right) \times 100 = -28\% \]

### Conclusion
Since the negative percentage indicates that the work was not completed as planned, we can conclude that 28% of the work remains incomplete by the end of the scheduled time.