In an examination, there were 1000 boys and 800 girls. 60% of the boys and 50% of the girls passed. Find the per cent of candidates failed.

Options

A. 0.464
B. 0.484
C. 0.444
D. 0.496

Answer

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

### Step 1: Calculate the total number of candidates
The total number of candidates is the sum of boys and girls.
- Total boys = 1000
- Total girls = 800

**Calculation:**
\[ \text{Total candidates} = \text{Total boys} + \text{Total girls} = 1000 + 800 = 1800 \]

### Step 2: Calculate the number of boys who passed
We know that 60% of the boys passed.
- Total boys = 1000
- Percentage of boys who passed = 60%

**Calculation:**
\[ \text{Passed boys} = \frac{60}{100} \times 1000 = 600 \]

### Step 3: Calculate the number of girls who passed
We know that 50% of the girls passed.
- Total girls = 800
- Percentage of girls who passed = 50%

**Calculation:**
\[ \text{Passed girls} = \frac{50}{100} \times 800 = 400 \]

### Step 4: Calculate the total number of candidates who passed
Now, we will find the total number of candidates who passed by adding the number of boys and girls who passed.

**Calculation:**
\[ \text{Total passed candidates} = \text{Passed boys} + \text{Passed girls} = 600 + 400 = 1000 \]

### Step 5: Calculate the number of candidates who failed
To find the number of candidates who failed, we subtract the total number of candidates who passed from the total number of candidates.

**Calculation:**
\[ \text{Failed candidates} = \text{Total candidates} - \text{Total passed candidates} = 1800 - 1000 = 800 \]

### Step 6: Calculate the percentage of candidates who failed
Finally, we will calculate the percentage of candidates who failed using the formula:

**Calculation:**
\[ \text{Percentage of failed candidates} = \left( \frac{\text{Failed candidates}}{\text{Total candidates}} \right) \times 100 \]
\[ = \left( \frac{800}{1800} \right) \times 100 \]
\[ = \frac{800 \times 100}{1800} = \frac{80000}{1800} \approx 44.44\% \]

### Final Answer
The percentage of candidates who failed is approximately **44.44%**.

---