In an examination, 49% students failed in English, 36% students failed in Hindi, while 15% failed in both. If total number of passed students is 450, then how many students did appear in the examination?

Options

A. 1800
B. 2000
C. 1100
D. 1500

Answer

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

### Step 1: Understand the given data
We know:
- Percentage of students who failed in English = 49%
- Percentage of students who failed in Hindi = 36%
- Percentage of students who failed in both subjects = 15%
- Number of students who passed = 450

### Step 2: Calculate the percentage of students who failed in either subject
To find the percentage of students who failed in either English or Hindi, we can use the principle of inclusion-exclusion:

\[ \text{Percentage failed in either subject} = (\text{Percentage failed in English}) + (\text{Percentage failed in Hindi}) - (\text{Percentage failed in both}) \]

Substituting the values:

\[ \text{Percentage failed in either subject} = 49\% + 36\% - 15\% = 70\% \]

### Step 3: Calculate the percentage of students who passed
If 70% of students failed, then the percentage of students who passed is:

\[ \text{Percentage passed} = 100\% - 70\% = 30\% \]

### Step 4: Set up the equation for total students
Let \( x \) be the total number of students who appeared for the examination. We know that 30% of \( x \) equals the number of students who passed:

\[ 0.30x = 450 \]

### Step 5: Solve for \( x \)
To find \( x \), we can rearrange the equation:

\[ x = \frac{450}{0.30} \]

Calculating this gives:

\[ x = 1500 \]

### Conclusion
The total number of students who appeared in the examination is **1500**.

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