A student got `28%` of the total marks and failed by `14` marks. Another student got `32%` marks and got `18`marks more than the pass marks. Find
(A) Max. marks
(B) Passing marks
(C ) Pass percentage

Options

A. `800,238,29.75%`
B. `700,228,39.75%`
C. `600,258,29.75%`
D. `500,268,49.75%`

Answer

To solve the problem step by step, let’s denote the maximum marks as \( M \) and the passing marks as \( P \).

### Step 1: Set up equations based on the information given.

1. The first student got \( 28\% \) of the total marks and failed by \( 14 \) marks.
\[ \text{Marks obtained by the first student} = 0.28M \]
\[ \text{Marks required to pass} = P \]
Since the first student failed by \( 14 \) marks, we can write:
\[ P = 0.28M + 14 \quad \text{(Equation 1)} \]

2. The second student got \( 32\% \) of the total marks and scored \( 18 \) marks more than the passing marks.
\[ \text{Marks obtained by the second student} = 0.32M \]
Since he got \( 18 \) marks more than the passing marks, we can write:
\[ 0.32M = P + 18 \quad \text{(Equation 2)} \]

### Step 2: Substitute Equation 1 into Equation 2.

From Equation 1, we know \( P \):
\[ P = 0.28M + 14 \]
Now substitute \( P \) into Equation 2:
\[ 0.32M = (0.28M + 14) + 18 \]
Simplifying this gives:
\[ 0.32M = 0.28M + 32 \]

### Step 3: Solve for \( M \).

Now, isolate \( M \):
\[ 0.32M - 0.28M = 32 \]
\[ 0.04M = 32 \]
\[ M = \frac{32}{0.04} = 800 \]

### Step 4: Find the passing marks \( P \).

Now that we have \( M \), substitute \( M \) back into Equation 1 to find \( P \):
\[ P = 0.28 \times 800 + 14 \]
\[ P = 224 + 14 = 238 \]

### Step 5: Calculate the pass percentage.

The pass percentage can be calculated using the formula:
\[ \text{Pass Percentage} = \left( \frac{P}{M} \right) \times 100 \]
Substituting the values we found:
\[ \text{Pass Percentage} = \left( \frac{238}{800} \right) \times 100 \]
\[ \text{Pass Percentage} = 29.75\% \]

### Final Answers:
(A) Maximum marks \( M = 800 \)
(B) Passing marks \( P = 238 \)
(C) Pass percentage \( = 29.75\% \)

---