in an examination there are 180 questions , 4 marks is given for each correct answers and 1 marks is subtracted for each wrong answers . if a boy scores 220 marks find the no of correct and wrong answers ???
If there are c correct and w wrong answers,
c+w=180
4c-w = 220
c=80
w=100
check: 4*80-100=220
To find the number of correct and wrong answers, we need to set up a system of equations based on the information given.
Let's assume the boy answered "x" questions correctly and "y" questions incorrectly.
According to the given information:
1. There are a total of 180 questions.
So, the correct and wrong answers should add up to 180.
Therefore, our first equation is: x + y = 180.
2. Each correct answer is awarded 4 marks, while each wrong answer deducts 1 mark.
The total score is given as 220 marks.
So, the equation for the total score is: 4x - y = 220.
Now we have a system of two equations:
Equation 1: x + y = 180
Equation 2: 4x - y = 220
We can solve this system of equations to find the values of x and y.
One method of solving this system is by elimination:
Multiply Equation 1 by 4 to make the coefficients of y in both equations the same.
4(x + y) = 4(180)
4x + 4y = 720 [Equation 3]
Now, add Equation 2 and Equation 3 to eliminate y:
(4x - y) + (4x + 4y) = 220 + 720
8x + 3y = 940 [Equation 4]
Now we have two equations:
Equation 4: 8x + 3y = 940
Equation 1: x + y = 180
We can solve this new system of equations to find the values of x and y.