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There are 180 multiple choice questions in a test. A candidate gets 4 marks for every correct answer, and for every un-attempted or wrongly answered questions, one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test, then how many questions did he answer correctly?

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Hint: Assign the number of un-attempted questions along with wrongly answered questions and the number of correct answers to two variables. Write two equations involving these variables for total number of questions and total marks obtained. Solve and find the number of correct answers.

Complete step-by-step answer:
Let the number of correctly answered questions be x and the number of un-attempted or wrongly answered questions be y.
It is given that the total number of questions in the test is 180, hence we have:
\[x + y = 180{\text{ }}...........{\text{(1)}}\]
The candidate gets 4 marks for every correct answer and -1 mark for every wrong answer or un-attempted question, so the total marks will be \[4x + ( - 1)y\] which is equal to 450.
\[4x + ( - 1)y = 450\]
\[4x - y = 450{\text{ }}...........{\text{(2)}}\]
Hence, we have two equations to solve two unknowns.
We want to find how many questions he answered correctly, that is, the variable x.
Add equation (1) and (2) and solve for x,
\[x + y + 4x - y = 180 + 450\]
The variable y cancels out, then we have:
\[5x = 630\]
\[x = \dfrac{{630}}{5}\]
\[x = 126\]
Hence, the number of questions he answered correctly is 126.

Note: You might also proceed by finding y first and then substituting in any one of the two equations and then finding x. It will be good to check your answer by substituting the values in both the equations.
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