In a test, +1 mark for a correct answer and \(\dfrac{1}{2}\) mark deducted for a wrong answer. Jayanti answered 120 questions and scored 90 marks. How many did she answer correctly?
\(100\) correct answers.
Step 1: Let the number of correct answers be \(c\).
Step 2: Then the number of wrong answers will be the rest, that is \(120 - c\).
Step 3: For every correct answer she gets +1 mark.
So, marks from correct answers = \(c\).
Step 4: For every wrong answer she loses half a mark (\(\tfrac{1}{2}\)).
So, marks lost from wrong answers = \(\tfrac{1}{2} \times (120 - c)\).
Step 5: Total score = (marks from correct answers) – (marks lost from wrong answers).
That means:
\[ \text{Score} = c - \tfrac{1}{2}(120 - c) \]
Step 6: We know her score is 90, so:
\[ c - \tfrac{1}{2}(120 - c) = 90 \]
Step 7: Expand the brackets:
\[ c - 60 + \tfrac{1}{2}c = 90 \]
Step 8: Combine like terms:
\[ 1.5c - 60 = 90 \]
Step 9: Add 60 on both sides:
\[ 1.5c = 150 \]
Step 10: Divide both sides by 1.5:
\[ c = 100 \]
Therefore, Jayanti answered 100 questions correctly.