Question

In a competitive examination ,5 marks are awarded for each correct answer, while 2 marks are deducted for each wrong answer. Jayant answered 120 questions and got 348 marks .How many questions did he answer correctly?​

Answer 1

Given :

• In a competitive examination ,5 marks are awarded for each correct answer, while 2 marks are deducted for each wrong answer

• Jayant answered 120 questions and got 348 marks .

To find :

• How many questions did he answer correctly

Solution :

Let us ,

Jayant is currently answered = x questions

Marks awarded for each question = 5

Therefore , Mark he got for with negative marking = 5x

Total answered of questions = 120

Now, Wrong answered questions

= [ 120 - x ]

Marks detected for each question = 2

Therefore, her total marks detected

= 2 [ 120 - x ] = 240 - 2x

Now ,

Marks obtained

= 5x - ( 240 - 2x )

= 5x - 240 + 2x

= 7x - 240

Let ,

7x - 240 + 2x

7x = 348 + 240 = 588

$\sf x = \frac{\cancel5\cancel8\cancel8}{\cancel7} = 84$

Therefore , She currently answered 84 questions .

Answer 2

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• 5 marks are awarded for each correct answer, while 2 marks are deducted for each wrong answer. Jayanth answered 120 questions and got 348 marks.

$\Large{\bf{\orange{\mathfrak{\dag{\underline{\underline{To \: find:-}}}}}}}$

• How many questions did he answer correctly?

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

• Let the number of correct answers be x.

• Let the number of incorrect answers be y.

• Jayanth answered 120 questions.

• $\implies$ x + y = 120

• x = 120 - y $\longrightarrow \: \boxed{1}$

Now,

• Jayanth scored 348 marks.

• Since, 2 marks are deducted for every wrong answer and 5 marks are awarded for every correct answer.

Therefore,

• 5x - 2y = 348 $\longrightarrow \: \boxed{2}$

Now,

• Substituting $\boxed{1}$ in $\boxed{2}$

• 5x - 2y = 348

• 5 (120 - y) - 2y = 348

• 600 - 5y - 2y = 348

• - 5y - 2y = 348 - 600

• - 7y = - 252

• $\sf y \: = \: \dfrac{- \: 252}{- \: 7}$

• $\sf y \: = \: \dfrac{\cancel{-} \: 252}{\cancel{-} \: 7}$

• $\sf y \: = \: \dfrac{\cancel{252}}{\cancel{7}}$

• $\boxed{\pink{\sf y \: = \: 36}}$

• Now the value that we have got is for incorrect answers.

• Correct answers =

• x + y = 120

• x + 36 = 120

• x = 120 - 36

• x = 84

Therefore,

• $\underline{\boxed{\therefore{\blue{\sf Jayanth \: answered \: 84 \: questions \: correctly.}}}}$