In an examination, ‘A’ scored `25%` of the total marks but failed by 56 marks and ‘B’ scored `50%`of the total marks which was 144 marks more than the minimum passing marks. What was the minimum passing marks for the examination ?

Options

A. 256
B. 196
C. 284
D. 180

Answer

To solve the problem step by step, we need to find the minimum passing marks based on the information provided about the scores of A and B.

### Step 1: Define the variables
Let the total marks of the examination be \( x \).

### Step 2: Determine A's score and passing marks
A scored 25% of the total marks, which can be expressed as:
\[ \text{A's score} = 0.25x \]
According to the problem, A failed by 56 marks, which means:
\[ \text{Minimum passing marks} = \text{A's score} + 56 = 0.25x + 56 \]

### Step 3: Determine B's score and passing marks
B scored 50% of the total marks, which can be expressed as:
\[ \text{B's score} = 0.50x \]
The problem states that B scored 144 marks more than the minimum passing marks, so we can write:
\[ \text{Minimum passing marks} = \text{B's score} - 144 = 0.50x - 144 \]

### Step 4: Set the two expressions for minimum passing marks equal to each other
Since both expressions represent the minimum passing marks, we can set them equal to each other:
\[ 0.25x + 56 = 0.50x - 144 \]

### Step 5: Solve for \( x \)
Rearranging the equation gives:
\[ 56 + 144 = 0.50x - 0.25x \]
\[ 200 = 0.25x \]
Now, multiply both sides by 4 to isolate \( x \):
\[ x = 200 \times 4 = 800 \]

### Step 6: Calculate the minimum passing marks
Now that we have the total marks \( x = 800 \), we can find the minimum passing marks using either expression. Let's use A's expression:
\[ \text{Minimum passing marks} = 0.25(800) + 56 \]
Calculating this gives:
\[ \text{Minimum passing marks} = 200 + 56 = 256 \]

### Final Answer
The minimum passing marks for the examination is **256**.

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