In an exam, a candidate secured 504 marks out of the maximum mark of 'M'. If the maximum mark 'M' is converted into 800 marks, he would have secured 384 marks. What is the value of 'M' ?

Options

A. A) 910
B. B) 1000
C. C) 970
D. D) None of the above

Answer

To solve the problem step by step, we will set up a proportion based on the information given in the question.

### Step 1: Set up the proportion
We know that the candidate scored 504 marks out of a maximum of M marks. If M is converted to 800 marks, the candidate would have scored 384 marks. We can set up the following proportion:

\[ \frac{504}{M} = \frac{384}{800} \]

### Step 2: Cross-multiply
To eliminate the fractions, we will cross-multiply:

\[ 504 \times 800 = 384 \times M \]

### Step 3: Calculate the left side
Now, we will calculate \(504 \times 800\):

\[ 504 \times 800 = 403200 \]

### Step 4: Write the equation
Now we can write the equation from our cross-multiplication:

\[ 403200 = 384 \times M \]

### Step 5: Solve for M
To find M, we will divide both sides of the equation by 384:

\[ M = \frac{403200}{384} \]

### Step 6: Perform the division
Now, we will perform the division:

\[ M = 1050 \]

### Final Answer
Thus, the value of M is:

\[ \boxed{1050} \]

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