The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of the failed candidates is 15, what is the number of candidates who passed the examination?

Answer

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

### Step 1: Understand the given information
We know:
- Total candidates = 120
- Average marks of all candidates = 35
- Average marks of passed candidates = 39
- Average marks of failed candidates = 15

### Step 2: Calculate the total marks obtained by all candidates
The total marks can be calculated using the formula:
\[ \text{Total Marks} = \text{Average Marks} \times \text{Total Candidates} \]
So,
\[ \text{Total Marks} = 35 \times 120 = 4200 \]

### Step 3: Set up the equations for passed and failed candidates
Let:
- \( x \) = number of candidates who passed
- \( y \) = number of candidates who failed

From the problem, we know:
\[ x + y = 120 \]

### Step 4: Calculate the total marks of passed and failed candidates
The total marks obtained by passed candidates:
\[ \text{Total Marks of Passed} = 39x \]
The total marks obtained by failed candidates:
\[ \text{Total Marks of Failed} = 15y \]

### Step 5: Set up the equation for total marks
The total marks from both passed and failed candidates should equal the total marks calculated:
\[ 39x + 15y = 4200 \]

### Step 6: Solve the equations
We have two equations:
1. \( x + y = 120 \)
2. \( 39x + 15y = 4200 \)

From the first equation, we can express \( y \) in terms of \( x \):
\[ y = 120 - x \]

Now substitute \( y \) in the second equation:
\[ 39x + 15(120 - x) = 4200 \]
Expanding this gives:
\[ 39x + 1800 - 15x = 4200 \]
Combining like terms:
\[ 24x + 1800 = 4200 \]
Subtracting 1800 from both sides:
\[ 24x = 2400 \]
Dividing by 24:
\[ x = 100 \]

### Step 7: Find the number of candidates who failed
Using the first equation:
\[ y = 120 - x = 120 - 100 = 20 \]

### Conclusion
The number of candidates who passed the examination is \( \boxed{100} \).

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