Question

A test consists of True' or 'False' questions. One mark is awarded for every correct answer while $\dfrac{1}{4}$ mark is deducted for every wrong answer. A student knew answers to some of the questions. Rest of the questions he attempted by cheating. He answered 120 questions and got 90 marks. It answers all questions he attempted by cheating were wrong, then how many questions did he answer correctly? How the habit of cheating will affect his character building?

Answer 1

Hint- To solve this question we use the basic two variable equation, so that we easily solve and get the answer. First, we need to assume the number of questions answered correctly be x and the number of questions answered incorrectly be y. and then after making a proper equation by using information given in this question as shown below.

Complete step by step solution:
Let the number of questions answered correctly be x
And the number of questions answered incorrectly be y
Total number of questions is equal to the sum of total number of correct answers and total number of incorrect answers.
As given in the question,
we have total 120 questions
That means, x + y = 120 ………………. (1)
Now,
Marks scored;
For correct answers is 1 mark × x answers = x marks
For incorrect answers -$\dfrac{1}{4}$ mark × y answers = -0.25y marks
Therefore, x +(- 0.25y) = 90 marks
                  = x - 0.25y = 90 ……………. (2)
We now have two equations and we use elimination methods.
Substitute x = 120 - y in the second equation and we get
 x - 0.25y = 90
120 - y - 0.25y = 90
30 = 1.25y
Y = 24
Now, put y=24 in equation (1), we get
x = 120 – y
x = 120- 24
x = 96
thus,
x = 96 and y = 24
therefore, the number of questions answered correctly be x = 96
And the number of questions answered incorrectly be y = 24.

Note-Equation is a convenient way to represent conditions or relations between two or more quantities. In this question, we have two variable equations and we know in a two-variable problem we rewrite the equations so that when the equations are added, one of the variables is eliminated, and then solved for the remaining variable.