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?
Question
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?
Solution
Sure, let's solve this step by step:
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The candidate attempted 8 questions and secured 50% marks in each of them. This means he got 4 marks for each question (since 50% of the total marks for each question, which is 8, is 4). So, the total marks he secured from these 8 questions is 8 * 4 = 32 marks.
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He obtained a total of 40% in the test. Let's assume the total number of questions in the test is 'x'. Since all questions carry equal marks, the total marks of the test is x * 8 (as each question carries 8 marks).
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According to the problem, 40% of the total marks is equal to 32 marks (which he got from 8 questions). So, we can set up the equation: 0.40 * (8x) = 32.
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Solving this equation for 'x' gives us the total number of questions in the test. Divide both sides of the equation by 80.40 to solve for 'x': x = 32 / (80.40) = 10.
So, there were 10 questions in the test.
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