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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? (a) 8 (b) 10 (c) 15 (d) 16



Answer :

rvkacademic

Answer:

There were a total of 10 questions in the test:
(b) 10

Step-by-step explanation:

Here is how to solve this problem:

  • Let's assume the total number of questions in the test is T
  • Let's also assume that each question carries 2 marks
  • Maximum marks possible = 2T marks
  • Candidate only attempted 8 questions and got 50%(1/2) of each question total marks
  • Therefore candidate got 1 mark per question for 8 questions for a total of 8 marks and 0 marks for each of the other questions resulting in an exam total of 8 marks
  • The overall percentage he obtained
    = Total marks received/Total marks possible
    = 8 / 2T
  • This overall percentage is given as 40% or in decimal = 0.40
  • Hence
    8/2T = 0.4
    8 = 2T * 0.4      => cross-multiply
    8 = 0.8T           ==> simplify right side
    T = 8/0.8          ==> switch sides and divide both sides by 0.8
    T = 10               ==> simplify

Therefore there were a total of 10 questions on the test

Verify

Let each test score be 10 points
Max possible = 10 * 10 = 100 points
8 questions answered at 50% => 8 questions at 5 points = 40 points
40 points/100 points = 0.40 = 40%

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