Question

For every correct answer, a student scores one mark but for every incorrect answer she/he loses 1/3 mark. She/He answered 108 questions but scored zero (0). How many questions she/he answered incorrectly?

(A)  81

(B)  78

(C)  87

(D)  72

Answer 1

Answer :-

$\bf\huge\boxed{(A) 81}$

Explanation :-

Given :

• Loses 1/3 for every incorrect answer.
• Scores 1 for every correct answer.
• No. of questions answered were 108.
• Scored marks was 0.

To find :

Number of questions answered incorrectly

Solution :

Let the number of question answered correctly be x

And the number of question answered incorrectly be y

Therefore, The first equation :-

$x + y = 108 \: .......(i)$

(The total number of answered questions were 108 so no. of answered questions correctly and incorrectly is added to the total)

And the second equation :-

$x - \dfrac{1}{3} \: of \: y = 0$

$x - \dfrac{y}{3} = 0 \: .......(ii)$

(The equation for the score he/she scored)

Now, we will solve the following equations by the substitution method.

=> x - y/3 = 0

=> x = y/3

=> 3x = y

As 3x = y, we will substitute the value of y in eqn.(i) by 3x

=> x + y = 108

=> x + 3x = 108

=> 4x = 108

=> x = 108/4

=> x = 27

And again, As 3x = y, Therefore :-

=> y = 3x

=> y = 3 × 27

=> y = 81

Hence, the no. of questions answered incorrectly were 81 respectively.

Answer 2

• Let the number of question answered correctly be M

And

• The number of question answered incorrectly be N

A.T.Q.

» He/she answered 108 questions including both correct and incorrect.

→ M + N = 108 _______ (eq 1)

» For every correct answer, a student scores one mark but for every incorrect answer she/he loses 1/3 marks.

→ M - $\dfrac{1}{3}$N = 0

→ M - $\dfrac{N}{3}$ = 0

→ M = $\dfrac{N}{3}$

→ 3M = N

→ N = 3M ______ (eq 2)

Put value of N in (eq 1)

→ M + 3M = 108

→ 4M = 108

→ M = $\dfrac{108}{4}$

→ M = 27 _________ ( eq 3)

Put value of M in (eq 2)

→ N = 3M

→ N = 3 (27)

→ N = 81

______________________________

He/she answered 81 questions incorrectly.

Option (A)

_________ [ ANSWER ]

______________________________