In a test, a candidate attempted only 8 questions and secured 50% marks in each of the questions. If he obtained a total of 40% in the test and all question in the test carried equal marks, how many questions were there in the test?

Correct Option (B)

Let 'M' represent the marks allotted for each question. Let 'N' be the total number of questions in the test.

• The candidate attempted 8 questions and secured 50% marks in each.
• The total marks obtained by the candidate from these 8 questions can be calculated as: $8\times (0.50\times M)=\mathbf{\text{4M}}$.
• The problem states that the candidate obtained a total of 40% in the test. The total marks for the entire test would be $N\times M$.
• Therefore, the marks obtained ($4M$) constitute 40% of the total test marks ($N\times M$).
• This relationship can be expressed as: $\text{textbf{4M = 0.40 times (N times M)}}$.
• Since 'M' represents marks per question and cannot be zero, we can divide both sides of the equation by 'M': $\text{textbf{4 = 0.40 times N}}$.
• Solving for N: $N=\frac{4}{0.40}=\mathbf{\text{10}}$.
• Hence, there were 10 questions in the test.

Incorrect Options:

• If the total number of questions was 8 (Option A), it would imply the candidate attempted all questions. In this scenario, scoring 50% in each question would result in a total score of 50% for the test, which contradicts the given condition of 40%.
• If the total number of questions was 15 (Option C), the total marks for the test would be $15M$. The percentage obtained by the candidate would be $\frac{4M}{15M}\times 100=\frac{4}{15}\times 100\approx \mathbf{\text{26.67\%}}$, which is not 40%.
• If the total number of questions was 16 (Option D), the total marks for the test would be $16M$. The percentage obtained by the candidate would be $\frac{4M}{16M}\times 100=\frac{1}{4}\times 100=\mathbf{\text{25\%}}$, which is not 40%.