In an examination , 40% of the candidates wrote their anwers in Hindi and the other in English . The average marks of the candidates written in Hindi is 74 and the average marks of the candidates written in English is 77. What is the average marks of all the candidates ?

Options

A. 75.5
B. 75.8
C. `76.0`
D. 76.8

Explanation

To find the average marks of all the candidates, we can follow these steps:

### Step 1: Determine the number of candidates who wrote in Hindi and English.
Let the total number of candidates be 100 (this simplifies calculations).

- Candidates who wrote in Hindi = 40% of 100 = 40 candidates
- Candidates who wrote in English = 100% - 40% = 60% of 100 = 60 candidates

### Step 2: Calculate the total marks for candidates who wrote in Hindi.
The average marks of candidates who wrote in Hindi is 74.

- Total marks for Hindi candidates = Average marks × Number of candidates
- Total marks for Hindi = 74 × 40 = 2960

### Step 3: Calculate the total marks for candidates who wrote in English.
The average marks of candidates who wrote in English is 77.

- Total marks for English candidates = Average marks × Number of candidates
- Total marks for English = 77 × 60 = 4620

### Step 4: Calculate the total marks of all candidates.
Now, we add the total marks of both groups:

- Total marks of all candidates = Total marks in Hindi + Total marks in English
- Total marks = 2960 + 4620 = 7580

### Step 5: Calculate the average marks of all candidates.
To find the average marks of all candidates, we divide the total marks by the total number of candidates:

- Average marks = Total marks / Total number of candidates
- Average marks = 7580 / 100 = 75.8

### Final Answer:
The average marks of all the candidates is **75.8**.

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