In a competitive exam, one mark is given for each accurate response, while $12$ mark is deducted for every wrong answer. Jayanti answered 120 questions and received 90 marks. How many questions did she successfully respond to?

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100

answer is D.

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Detailed Solution

It is given that Jayanti completed 120 questions correctly and received 90 marks in a competitive test where one mark is given for each correct response and half a mark is subtracted for each incorrect response.
Let there were

p

correct answers and

q

incorrect answers.
The equation for Jayanti's overall number of questions is,

⇒ p + q = 120

…(1)
The equation for total marks got by Jayanti is,

⇒ p × 1 − 12 q = 90 ⇒ p − 0.5 q = 90 − e q .2)

Subtracting equation (2) from equation (1) we get,

⇒ p + q − p − − 0.5 q = 120 − 90 ⇒ 1.5 q = 30 ⇒ q = 20

Substitute

q = 20

in equation (1) we get,

p + 20 = 120

\Rightarrow p = 100

Therefore, Jayanti answered 100 questions correctly.
Hence, option (4) is correct.

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