1200 boys and 600 girls are examined in a test. `42%` of the boys and `30%` of the girls passed. Find the percentage of those who failed.

Answer

To find the percentage of students who failed the test, we can follow these steps:

### Step 1: Determine the number of boys who passed the test.
- Total number of boys = 1200
- Percentage of boys who passed = 42%

To find the number of boys who passed:
\[ \text{Number of boys who passed} = \frac{42}{100} \times 1200 = 504 \]

### Step 2: Determine the number of girls who passed the test.
- Total number of girls = 600
- Percentage of girls who passed = 30%

To find the number of girls who passed:
\[ \text{Number of girls who passed} = \frac{30}{100} \times 600 = 180 \]

### Step 3: Calculate the total number of students who passed the test.
\[ \text{Total passed} = \text{Number of boys who passed} + \text{Number of girls who passed} = 504 + 180 = 684 \]

### Step 4: Calculate the total number of students examined.
\[ \text{Total students} = \text{Total boys} + \text{Total girls} = 1200 + 600 = 1800 \]

### Step 5: Determine the total number of students who failed the test.
\[ \text{Total failed} = \text{Total students} - \text{Total passed} = 1800 - 684 = 1116 \]

### Step 6: Calculate the percentage of students who failed the test.
\[ \text{Percentage of students who failed} = \left( \frac{\text{Total failed}}{\text{Total students}} \right) \times 100 = \left( \frac{1116}{1800} \right) \times 100 \approx 62 \]

### Final Answer:
The percentage of students who failed the test is approximately **62%**.

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