Answer
Verified
425.4k+ 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
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Summary of the poem Where the Mind is Without Fear class 8 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Write an application to the principal requesting five class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE