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?
- A8
- B10Correct
- C15
- D16
Explanation
Let 'N' be the total number of questions in the test. Let 'M' be the marks allotted for each question. So, the total maximum marks for the test = N * M.
The candidate attempted only 8 questions. In each of these 8 questions, he secured 50% marks. Marks obtained in one question = 50% of M = 0.5 * M. Total marks obtained by the candidate = 8 questions * (0.5 * M marks/question) = 4M.
The candidate obtained a total of 40% in the test. This means (Total marks obtained) / (Total maximum marks) = 40%. So, (4M) / (N * M) = 0.40.
We can cancel 'M' from both the numerator and the denominator: 4 / N = 0.40.
Now, solve for N: N = 4 / 0.40 N = 4 / (4/10) N = 4 * (10/4) N = 10.
Therefore, there were 10 questions in the test.
Analyzing the options: A) 8: If there were 8 questions, and he got 50% in each of the 8, his total score would be 50%, not 40%. This is incorrect. B) 10: This matches our calculated value. If there are 10 questions (total 10M marks) and he scored 4M, his percentage is (4M/10M) * 100 = 40%. This is correct. C) 15: If there were 15 questions (total 15M marks) and he scored 4M, his percentage would be (4M/15M) * 100 = 26.67%, not 40%. This is incorrect. D) 16: If there were 16 questions (total 16M marks) and he scored 4M, his percentage would be (4M/16M) * 100 = 25%, not 40%. This is incorrect.
The final answer is B.
Related questions
More UPSC Prelims practice from the same subject and topic.
- Prelims 2015CSATQuantitative Aptitude
A father is nine times as old as his son and the mother is eight times as old as the son. The sum of the father's and the mother's age is 51 years. What is the age of the son?
- Prelims 2015CSATQuantitative Aptitude
Each of A, B, C and D has Rs 100. A pays Rs 20 to B, who pays Rs 10 to C, who gets Rs 30 from D. In this context, which one of the following statements is not correct?
- Prelims 2015CSATQuantitative Aptitude
Two equal glasses of same type are respectively 1/3 and 1/4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot?
- Prelims 2015CSATQuantitative Aptitude
In a parking area, the total number of wheels of all the cars (four- wheelers) and scooters/motorbikes (two-wheelers) is 100 more than twice the number of parked vehicles. The number of cars parked is
- Prelims 2015CSATQuantitative Aptitude
A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair. While preparing the bill, the bill clerk interchanged the number of bl…
- Prelims 2015CSATQuantitative Aptitude
The monthly incomes of Peter and Paul are in the ratio of 4:3. Their expenses are in the ratio of 3:2. If each saves Rs. 6,000 at the end of the month, their monthly incomes respectively are (in Rs.)