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 questions in the test carried equal marks, how many questions were there in the test’?

The correct option is 10.

Let us break down the problem step-by-step to understand why this is the correct answer:

Step 1: Understand the marks obtained in the attempted questions
Let the maximum marks for each question in the test be M.
Since all questions carry equal marks, each question is worth M marks.
The candidate attempted exactly 8 questions and secured 50% marks in each of them.
Therefore, the marks secured in each attempted question is:

$$50\%\text{of}M=0.5M$$
Since the candidate attempted 8 questions, the total marks obtained by the candidate is:

$$\text{Total Marks Obtained}=8\times 0.5M=4M$$

Step 2: Relate the obtained marks to the total marks of the test
Let the total number of questions in the test be N.
Since each question carries M marks, the total maximum marks for the entire test is:

$$\text{Total Maximum Marks}=N\times M$$
We are given that the candidate obtained a total of 40% in the test. This means:

$$\text{Total Marks Obtained}=40\%\text{of}(N\times M)$$
Substituting the value from Step 1, we get:

$$4M=0.4\times N\times M$$

Step 3: Solve for the total number of questions (N)
Since M (marks per question) is a positive non-zero value, we can divide both sides of the equation by M:

$$4=0.4\times N$$
Solving for N:

$$N=\frac{4}{0.4}$$
Thus, there were a total of 10 questions in the test.