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?
Last updated date: 26th Mar 2023
•
Total views: 307.8k
•
Views today: 5.84k
Answer
307.8k+ views
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.
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.
Recently Updated Pages
If abc are pthqth and rth terms of a GP then left fraccb class 11 maths JEE_Main

If the pthqth and rth term of a GP are abc respectively class 11 maths JEE_Main

If abcdare any four consecutive coefficients of any class 11 maths JEE_Main

If A1A2 are the two AMs between two numbers a and b class 11 maths JEE_Main

If pthqthrth and sth terms of an AP be in GP then p class 11 maths JEE_Main

One root of the equation cos x x + frac12 0 lies in class 11 maths JEE_Main

Trending doubts
What was the capital of Kanishka A Mathura B Purushapura class 7 social studies CBSE

Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Tropic of Cancer passes through how many states? Name them.

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

Name the Largest and the Smallest Cell in the Human Body ?
