Question

A test contains 10 true/false questions. A correct answer is awarded 2 marks, a wrong answer -1 and a question not answered is awarded 0. A student attempts 7 questions and gets 8 marks. How many questions did the student answer correctly?

Answer 1

Hint: Consider the answers which are correct as ‘x’ and which are incorrect as ‘y’. Student attempted 7 questions which means $x + y = 7$. Each correct answer is awarded with 2 marks which means the total no. of marks for correct answers is 2x and for incorrect -1, which means –y. Total marks student secured is 8 i.e. $2x - y = 8$ . Solve these two equations to find the no. of questions the student answered correctly.


Complete step-by-step Solution:
We are given that there are 10 true/false questions in a test. A correct answer is awarded 2 marks, and incorrect answer is awarded -1 marks and a question not answered is awarded 0.
A student attempts 7 questions and gets 8 marks. We have to find the no. of questions the student answered correctly.
Let the no. of questions in which the student answered correctly is ‘x’ and no. of questions answered incorrectly is ‘y’.
No. of marks awards for correct answers will become 2x and marks for incorrect answers will become –y.
Total no. of questions answered is 7, i.e. $x + y = 7$ $ \to eq(1)$
Total no. of marks obtained is 8, i.e. $2x - y = 8$ $ \to eq(2)$
Solve eq (1) and eq (2)
$
  2x - y = 8 \\
  y = 2x - 8 \to eq(3) \\
 $
Substitute eq (3) in eq (1)
$
  x + y = 7 \\
  y = 2x - 8 \\
   \to x + 2x - 8 = 7 \\
  3x - 8 = 7 \\
  3x = 15 \\
  x = \dfrac{{15}}{3} \\
  x = 5 \\
  y = 2x - 8 \\
   \to y = \left( {2 \times 5} \right) - 8 \\
  y = 10 - 8 \\
  y = 2 \\
 $
Therefore, the no. of questions the student answered correctly is 5 and incorrectly is 2.


Note: In this question, the linear equations are solved using substitution method. Linear equations with two variables can also be solved using the Graphing method and elimination method.