Question

: In a competitive exam, one mark is added for each correct answer while half a mark is deducted for every wrong answer. Jayanti answered 120 questions and got 90 marks. How many questions did she answer correctly?
A)70
B)125
C)66
D)100

Answer 1

Hint: This is a question of linear equations in a single variable. Here we will first assume a suitable variable from the unknown values and then form a suitable equation according to the question. We will then solve the equation to get the final answer.

Complete step-by-step answer:

Let the total number of questions Jayanti answered correctly be x. She answered a total of 120 questions, so the number of questions she answered incorrectly are 120 - x. She gets one mark for every correct answer and loses half a mark for an incorrect answer. So, the total number of marks obtained by her should be-

1(x) - 0.5(120 - x)

We have been given that the she obtained 90 marks so-

1(x) - 0.5(120 - x) = 90

Solving the equation for x we get-

x - 60 + 0.5x = 90

1.5x = 90 + 60 =150

x = 100

x was assumed to be the number of correct answers, which is the final answer. Hence, the correct option is D. 100.

Note: In such types of questions, try to assume the final answer as your variable because it makes it easier to solve the problem. In this question, we can assume the number of incorrect answers to be x and the correct answers 120 - x. So the equation will be-

1(120 - x) -0.5x = 90
1.5x = 30
x = 20, 120 - x = 100.
The final answer remains the same.