Question

In a competition, (+5) marks are given for every correct answer and (-2) marks for every incorrect answer. Anjali answered all the questions and scored 30 marks. If she got 10 correct answers, how many questions did she answer incorrectly?
A. 20
B. 10
C. 5
D. 8

Answer 1

Hint: We will first assume the number of total questions that we have in the paper. After that, we will assume the number of correct answers she gave. Now, we will use the given conditions to form the equations and thus find the answer.

Complete answer:
Let us assume that there were a total of x questions in the test paper in all.
This means that she answered ‘x’ number of questions in the paper.
Since it is given that she gave 10 correct answers in the test paper. Therefore, the number of incorrect answers will be ‘x – 10’.
Now, since, each correct answer is awarded +5 and each incorrect answer is awarded -2, so, she will obtain marks: 5(10) – 2(x – 10)
Now, since it is already given to us that she has scored a total of 30 marks.
$ \Rightarrow $5(10) – 2(x – 10) = 30
Simplifying the calculation on the left hand side by opening the parenthesis and doing the multiplication as required, we will get the following expression:-
$ \Rightarrow $50 – 2x + 20 = 30
Simplifying by clubbing the like terms on the left hand side and adding them, we will then obtain:-
$ \Rightarrow $70 – 2x = 30
Rearranging the terms in the above expression to obtain the following expression:-
$ \Rightarrow $ 2x = 70 – 30
Simplifying by doing the calculations on the right hand side, we will then obtain:-
$ \Rightarrow $ 2x = 40
Dividing both the sides by 2 in the above expression, we will then get:-
$ \Rightarrow $ x = 20

Hence, there were a total of 20 questions in the test paper.

Note:
The students must note that they must assume the total number of questions to be some alphabet because it made our task very easy as in the above solution.
The students must also note that, in the above solution, we had one variable ‘x’ and thus, we formed one equation to find its value. We need to use as many equations as many numbers of variables we got to use in a question. Now, if you would have assumed the correct answers to be another alphabet ‘y’, then we have got the equation y = 10 as well. Two variables means two solutions and thus an answer.