Let the total number of questions in the test be N. Each question carries equal marks, so the total marks in the test are proportional to N.

Given:

• The candidate attempted 8 questions and secured 50% marks in each.
• He obtained a total of 40% in the test.
• All questions in the test carried equal marks.

Solution:

1. Marks per question:

• Let the total marks for the test be M.
• Since all questions carry equal marks, each question is worth $M/N$ marks.

2. Marks obtained by the candidate:

• The candidate attempted 8 questions and secured 50% marks in each.
• Therefore, the marks obtained in each attempted question are $0.5 \cdot (M/N) = M/(2N)$.
• Total marks obtained by the candidate = $8 \cdot (M/(2N)) = 4M/N$.

3. Total marks obtained as a percentage:

• The candidate obtained 40% of the total marks.
• Therefore, $4M/N = 0.4 \cdot M$.

4. Solving for N:

• Simplifying the equation: $4M/N = 0.4 \cdot M$ $4/N = 0.4$ $N = 4/0.4 = 10$.

Therefore, the total number of questions in the test is $N = 10$.