Question

59. In a competitive exam, 3 marks are given for each correct answer and 1 mark is
subtracted for each wrong answer. In a test paper of 50 questions Riya got 78
marks. Then for how many questions she write the correct answers ?
(1) 42
(2) 38
(3) 32
(4) 18​

Answer 1

Given :-

• (+3) marks are given for each correct answer
• (-1) is deducted for every wrong answer
• The question paper contains 50 questions

Riya scored 78 marks

Aim :-

• To find the number of questions answered correctly by Riya

ANSWER :-

→ The total marks obtained for 50 questions will be :-

→ 50 × 3

→ 150 marks

Method 1 :-

• Total marks = 150
• Riya's marks = 78

Total marks Riya lost :- 150 - 78

→ 72 marks

When a question is answered wrong, a student looses :- (-3) + (-1) = (-4) marks

[As no marks are given for a wrong answer and (-1) is lost for each wrong answer]

If Riya lost 72 marks, then number of questions answered wrongly is :-

$\implies \dfrac{72 }{4}$

Reducing to the lowest terms,

$\implies 18$

Therefore Riya answered 18 questions wrong.

Number of questions answered correctly :- (Total questions) - (Questions answered wrong)

→ 32 questions.

Method 2 :-

• Let the total number of questions answered correctly be x
• The total number of Questions answered wrongly is then y

According to the question,

x + y = 50 → Equation 1

If (+3) marks is given for each correct answer then marks obtained for each correct answer will be (+3) × x → 3x

If (-1) marks is deducted for each wrong answer, then marks deduced for each wrong answer will be (-1) × y → (-y)

The difference between the 2 marks will be 78.

3x - y = 78 → Equation 2

Now that we have 2 Equations, let's solve the value for x and y respectively.

Equation 1 :-

x + y = 50

Transposing x to the other side,

➵y = 50 - x

Equation 2 :-

3x - y = 78

By substituting the value of y as 50 - x,

➵ 3x - (50 - x) = 78

By opening the brackets,

➵ 3x - 50 + x = 78

Adding the variables,

➵ 4x - 50 = 78

Transposing (-50),

➵ 4x = 78 + 50

➵ 4x = 128

Transposing 4,

$\implies \dfrac{128}{4}$

Reducing to the lowest terms we get

→ x = 32

As we assumed all the correct answers to be x, the number of correct answers given by Riya is 32.

Verification :-

Let us verify the answer by subtracting the total marks obtained for the wrong answers by the correct answers.

➵ (3 × 32) - (1 × 18)

➵ 96 - 18

➵ 78

Hence Verified

Option (3) 32 is correct.