The average of marks obtained by 125 candidates in a certain examination is 29. If the average marks of passed candidates is 36 and that of the failed candidates is 11, what is the number of candidates who failed the examination ?

Answer

To find the number of candidates who failed the examination, we can use the concept of allegation. Here's the step-by-step solution:

### Step 1: Understand the Given Information
- Total number of candidates = 125
- Average marks of all candidates = 29
- Average marks of passed candidates = 36
- Average marks of failed candidates = 11

### Step 2: Set Up the Allegation
We will use the allegation method to find the ratio of passed to failed candidates. The average marks of passed candidates (36) is the higher value, the average marks of failed candidates (11) is the lower value, and the overall average (29) is the middle value.

### Step 3: Calculate the Differences
- Difference between passed candidates' average and overall average:
\[ 36 - 29 = 7 \]

- Difference between overall average and failed candidates' average:
\[ 29 - 11 = 18 \]

### Step 4: Set Up the Ratio
Using the differences calculated:
- The ratio of passed candidates to failed candidates is:
\[ \text{Ratio} = \frac{18}{7} \]

### Step 5: Calculate Total Parts
The total parts in the ratio:
\[ 18 + 7 = 25 \]

### Step 6: Find the Value of One Part
Since the total number of candidates is 125, we can find the value of one part:
\[ \text{Value of one part} = \frac{125}{25} = 5 \]

### Step 7: Calculate the Number of Failed Candidates
Now, we can find the number of failed candidates using the ratio:
\[ \text{Number of failed candidates} = 7 \times 5 = 35 \]

### Final Answer
The number of candidates who failed the examination is **35**.

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