In the Polo hospital some pateints who were suffering from the Hepatites-B were admitted for the treatment, but 9% of the patients were died within half an hour. After treatment, the percentage of patients cured out of the remaining was only 80%. Out of these patients only 70% are completely cured out and the remaining were partially cured out which were equal to 153 patients. The no. of patients (approx.) who were admitted for the treatment for the same was :

Options

A. 400
B. 678
C. 560
D. 700

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the total number of patients admitted
Let the total number of patients admitted to the hospital be \( x \).

### Step 2: Calculate the number of patients who died within half an hour
According to the problem, 9% of the patients died within half an hour. Therefore, the number of patients who died is:
\[ \text{Patients died} = 0.09x \]

### Step 3: Calculate the number of remaining patients
The remaining patients after the deaths are:
\[ \text{Remaining patients} = x - 0.09x = 0.91x \]

### Step 4: Calculate the number of patients cured
Out of the remaining patients, 80% were cured. Thus, the number of patients cured is:
\[ \text{Patients cured} = 0.80 \times 0.91x = 0.728x \]

### Step 5: Determine the number of completely and partially cured patients
Out of the cured patients, 70% were completely cured and 30% were partially cured. Therefore:
- The number of completely cured patients is:
\[ \text{Completely cured} = 0.70 \times 0.728x = 0.5096x \]
- The number of partially cured patients is:
\[ \text{Partially cured} = 0.30 \times 0.728x = 0.2184x \]

### Step 6: Set up the equation based on the number of partially cured patients
According to the problem, the number of partially cured patients equals 153. Thus, we can set up the equation:
\[ 0.2184x = 153 \]

### Step 7: Solve for \( x \)
To find \( x \), we divide both sides of the equation by 0.2184:
\[ x = \frac{153}{0.2184} \approx 700 \]

### Conclusion
The approximate number of patients who were admitted for treatment was:
\[ \boxed{700} \]