Question

There are 90 multiple choice questions in a test. Two marks are awarded for every correct answer and one mark is deducted for every wrong answer. If Sahana got 60 marks in the test while she answered all the questions, then how many questions did she answer correctly?

Answer 1

Hint: To find the number of correct questions answered by Sahana, let us assume this to be x. We know that total number of questions =90 . Hence, the number of incorrectly answered questions \[=90-x\] . It is given that 2 marks are awarded for every correct answer. Hence, we get the number of marks scored for correct answers =2x . We know that 1 mark is deducted for every wrong answer which gives the number of marks to be deducted for wrong answers $=\left( 90-x \right)\times 1=\left( 90-x \right)$ . The total marks scored by Sahana is $2x-\left( 90-x \right)=60$ . We have to find the value of x which is the required answer.

Complete step-by-step answer:
We have to find the number of correct questions answered by Sahana.
We have, total number of questions =90
Let us assume x to be the number of questions answered correctly. Then, we can find the number of incorrectly answered questions by subtracting x from 90.
Number of incorrectly answered questions \[=90-x\]
It is given that 2 marks are awarded for every correct answers. Hence, we can get the number of marks scored for correct answers as shown below.
Number of marks scored for correct answers =2x
We know that 1 mark is deducted for every wrong answer. Hence, the number of marks to be deducted for wrong answers is given by
Number of marks to be deducted for wrong answers $=\left( 90-x \right)\times 1=\left( 90-x \right)$
We know that Sahana scored 60 marks. Hence, we can write the total marks scored by Sahana as
\[\text{Number of marks for correct answers}-\text{number of marks for wrong answers}=\text{Marks scored by Sahana}\]Let us now substitute the values. We will get
$\begin{align}
  & 2x-\left( 90-x \right)=60 \\
 & \Rightarrow 2x-90+x=60 \\
\end{align}$
Let us collect the constants to one side and variables in the other.
$2x+x=60+90$
Let us solve this.
$\begin{align}
  & 3x=150 \\
 & \Rightarrow x=\dfrac{150}{3} \\
 & \Rightarrow x=50 \\
\end{align}$
Hence, the number of correct questions answered by Sahana is 50.

Note: You must always take the parameter to be found as always x. You may make mistakes by writing the number of marks to be deducted for wrong answers as $=\left( 90-x \right)-1$ . There can be a chance of error when writing the total marks scored by Sahana as $2x-\left( 90-x \right)=60$ .