Question

 In an examination A got 38% marks and failed by 42 marks. While B got 25% more marks than A and passed by 15 marks. What is the passing percentage for the examination ?
1. 45%
2. 43%
3. 48%
4. 51%

Answer 1

Correct Answer - Option 1 : 45%

Given:

In an examination A got 38% marks and failed by 42 marks. While B got 25% more marks than A and passed by 15 marks. 

Concept used:

Percentage

Calculation:

Let the maximum marks for the examination be a.

Marks scored by A

⇒ \(\frac{{38}}{{100}} × a = \frac{{19a}}{{50}}\)

Marks scored by B

⇒ \(\frac{{19a}}{{50}} × \frac{{125}}{{100}} = \frac{{95a}}{{200}}\)

As per the question, 

⇒ \(\frac{{19a}}{{50}} + 42 = \frac{{95a}}{{200}} - 15\) {Keeping the passing marks same.}

⇒ \(\frac{{95a}}{{200}} - \frac{{19a}}{{50}} = 57\)

⇒ \(\frac{{19a}}{{200}} = 57\)

⇒ a = 3 × 200 = 600

Passing marks = \(\left( {600 \times \frac{{19}}{{50}}} \right) + 42\) = 270

∴ Required passing percentage = \(\frac{{270}}{{600}} \times 100 = 45\% \)