# Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. - Mathematics

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method

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 awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test?

#### Solution

Let the number of right answers and wrong answers be x and y respectively.

According to the question,

3x - y = 40 ... (i)

4x - 2y = 50

⇒ 2x - y = 25 ... (ii)

Subtracting equation (ii) from equation (i), we get

x = 15 ... (iii)

Putting this value in equation (ii), we get

30 - y = 25

y = 5

Therefore, number of right answers = 15

And number of wrong answers = 5

Total number of questions = 20

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Cross - Multiplication Method
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#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.5 | Q 4.3 | Page 63