Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awanded for each correct answer and 2 marks been deducted for each incorrect answer, the Yash would have scored 50 marks. How many question were there in the test?
Answers
Given : Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awanded for each correct answer and 2 marks been deducted for each incorrect answer, the Yash would have scored 50 marks.
Solution:
Let the number of right answers be x
And number of Wrong answers be y.
Total number of questions in the test = x + y
CONDITION 1 :
Marks awarded for x right answers= 3x
Marks lost for y wrong answers = y×1= y
3x - y = 40………….(1)
CONDITION 2 :
Marks awarded for x right answers= 4x
Marks lost for y wrong answers = y×2= 2y
4x - 2y = 50…………(2)
Multiply equation 1 by 2 and subtract equation 2 :
6x - 2y = 80
4x - 2y = 50 [By elimination method]
(-) (+) (-)
-----------------
2x = 30
x = 30 /2
x = 15
On putting the value of x in equation 1 :
3x - y = 40
3(15) - y = 40
45 - y = 40
-y = 40 - 45
-y = - 5
y = 5
Total number of questions in the test = x + y = 20 + 5 = 25.
Hence, there were total 25 questions in the test
Hope this answer will help you…
Some more questions from this chapter :
Pinky scored 40 marks in a test getting 3 marks for each right answer and losing 1 mark for each wrong answer.Had 4 marks been awarded for each correct answer and 2 marks were deducted for each wrong answer, then pinky again would have scored 40 marks. How many questions were there in the test?
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Raju used 2 plastic bags and 1 paper bag in a day which cost him ₹ 35. While Ramesh used 3 plastic bags and 4 paper bags per day, which cost him ₹ 65 (i) Find the cost of each bag. (ii) Which bag has to be used and what value is reflected by using it.
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Answer:
Step-by-step explanation:
Solution:-
Let number of correct answers be x
And the number of incorrect answers be y.
According to the Question,
⇒ 3x - y = 40 … (i)
⇒ 4x - 2y = 50 … (ii)
Solving Eq (i) and (ii), we get
⇒ 6x - 2y = 80 … (iii)
Subtracting (ii) from (iii), we get,
⇒ 2x = 30
⇒ x = 30/2
⇒ x = 15
Putting x's value in Eq (i), we get
⇒ 3x - y = 40
⇒ 3(15) - y = 40
⇒ 45 - y = 40
⇒ y = 45 - 40
⇒ y = 5
Total number of questions = 15 + 5 = 20
Hence, 20 question were there in the test.