Question

P scored $30%$ marks and failed by 30 marks, Q scored $40%$ marks and obtained 40 marks more than those required to pass. The pass percentage is:

• A. 32%
• B. 34.2%
• C. 36%
• D. 38%

Hint:

Alternatively, look at the difference in percentages and marks directly:
Difference in percentage $= 40% - 30% = 10%$
Difference in marks $= 40 - (-30) = 70$ marks
Therefore, $10% = 70$ marks, which implies $1% = 7$ marks.
To pass, P needs 30 more marks, which is equal to:
\[ \frac{30}{7} \approx 4.28% \]
Pass Percentage $= 30% + 4.28% = 34.28% \approx 34.2%$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The problem gives the score of two students, P and Q, relative to the passing marks.
P scored $30%$ of the maximum marks and fell short of passing by 30 marks.
Q scored $40%$ of the maximum marks and exceeded the passing marks by 40 marks.
We need to determine the passing percentage required to clear the examination.

Step 2: Key Formula or Approach:
Let the maximum marks of the examination be \(x\).
The passing marks can be expressed in two ways based on the scores of P and Q:
\[ \text{Passing Marks} = (30% \text{ of } x) + 30 = (40% \text{ of } x) - 40 \]
By equating these two expressions, we can find the maximum marks \(x\), and then find the passing percentage.

Step 3: Detailed Explanation:
$\bullet$ Finding the Maximum Marks (x):
Set up the equation equating passing marks:
\[ \frac{30}{100}x + 30 = \frac{40}{100}x - 40 \]
\[ 0.3x + 30 = 0.4x - 40 \] Rearranging the terms:
\[ 0.4x - 0.3x = 30 + 40 \]
\[ 0.1x = 70 \]
\[ x = \frac{70}{0.1} = 700 \]
The maximum marks for the examination is 700.
$\bullet$ Finding the Passing Marks:
Now, substitute \(x = 700\) back into either expression to find the passing marks:
\[ \text{Passing Marks} = 0.3(700) + 30 \]
\[ \text{Passing Marks} = 210 + 30 = 240 \]
The passing mark is 240.
$\bullet$ Calculating the Pass Percentage:
The pass percentage is the ratio of the passing marks to the maximum marks, expressed as a percentage:
\[ \text{Pass Percentage} = \left( \frac{\text{Passing Marks}}{\text{Maximum Marks}} \right) \times 100 \]
\[ \text{Pass Percentage} = \left( \frac{240}{700} \right) \times 100 \]
\[ \text{Pass Percentage} = \frac{240}{7} \approx 34.28% \]
Comparing this with the options, Option (B) is $34.2%$.

Step 4: Final Answer:
The pass percentage for the examination is approximately $34.2%$.