In a test a candidate secured 336 marks out of maximum marks 'x'. If the maximum marks 'x' were converted into 400 marks he would have secured 192 marks. What were the maximum marks of the test?

Options

A. 700
B. 750
C. 500
D. 650

Answer

To solve the problem, we need to find the maximum marks 'x' based on the information provided. Here’s a step-by-step breakdown of the solution:

### Step 1: Set up the relationship
The candidate scored 336 marks out of a maximum of 'x' marks. When these marks are converted to a scale of 400, the candidate would have scored 192 marks. We can set up a proportion based on this information.

### Step 2: Write the proportion
The proportion can be expressed as:
\[ \frac{336}{x} = \frac{192}{400} \]

### Step 3: Cross-multiply to solve for 'x'
Cross-multiplying gives us:
\[ 336 \times 400 = 192 \times x \]

### Step 4: Calculate the left side
Calculating the left side:
\[ 336 \times 400 = 134400 \]

### Step 5: Set up the equation
Now we have:
\[ 134400 = 192x \]

### Step 6: Solve for 'x'
To find 'x', divide both sides by 192:
\[ x = \frac{134400}{192} \]

### Step 7: Perform the division
Calculating the division:
\[ x = 700 \]

### Conclusion
The maximum marks of the test are **700**.

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