Question

Q36. 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.

Answer 1

Let the number of right answers be $\longrightarrow$ x

Let the number of wrong answers be $\longrightarrow$ y

ATQ,

3x - y = 40 → Eq1

4x - 2y = 50 → Eq2

Now, Multiplying Equation 1 by 2 we get,

6y - 2y = 80 → 3

Now, We subtract Equation 1 from Equation 3.

$\sf 6y - 2y = 80\\ \\\sf 4x - 2y = 50\\\rule{2cm}{1}\\ \\\sf 2x = 30\\ \\\ x = \dfrac{30}{2}\\ \\x = 15$

$\huge\boxed{\sf x = 15}$

Now we substitute the value of 'x' in Equation 1.

3x - y = 40

3(15) - y = 40

45 - y = 40

45 - 40 = y

5 = y

$\huge\boxed{\sf y = 5}$

Answers:

Number of right answers $\longrightarrow$ 15

Number of wrong answers $\longrightarrow$ 5

Hence the Total number of questions $\longrightarrow$ 20.

Answer 2

Answer:

$\huge{\mathcal{\underline{\green{Answer}}}}$

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

∴ According to the question ,

3x−y=40⟶(i)

and , 2x−y=25⟶(ii)

On substraction : x=15

putting the value of x in ⟶(i)

3(15)−y=40

y=5

∴ Number of right answers=15 answers

Number of wrong answers=5 answers.

Total Number of questions 5+15=20