Question

In a competitive exam, 5 marks are awarded for every correct answer and for every wrong answer, 2 marks are deducted. Sathwik scores 32 marks in the examination. If 4 marks had been awarded for each correct answer and 1 mark had been deducted for each incorrect answer, Sathwik would have scored 34 marks. If Sathwik attempted all the questions, how many questions were there in the test ?

14

12

20

26

​

Answer 1

ANSWER IS

x=12 and y= 14

x+y=12+14=26

answer =26

26

Answer 2

SOLUTION :

GIVEN

• In a competitive exam, 5 marks are awarded for every correct answer and for every wrong answer, 2 marks are deducted. Sathwik scores 32 marks in the examination.

• If 4 marks had been awarded for each correct answer and 1 mark had been deducted for each incorrect answer,

• Sathwik would have scored 34 marks.

TO DETERMINE

The number questions were there in the test if Sathwik attempted all the questions,

CALCULATION

Let Sathwik answered x questions right and y question wrong.

Then total number of questions = x + y

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

The marks Sathwik scores in the examination

$= \sf{}5x - 2y$

So

$\sf{}5x - 2y = 32 \: \: \: \: \: ........(1)$

Now if 4 marks are awarded for every correct answer and for every wrong answer, 1 marks are deducted.

marks are deducted. The marks Sathwik scores in the examination

$= \sf{}4x - y$

So

$\sf{}4x - y = 34 \: \: \: .....(2)$

Now we solve for x and y

Now Equation (1) - 2×Equation (2) gives

$\sf{}5x - 2y - 8x + 2y = 32 -76$

$\implies \sf{} - 3x = - 36$

$\implies \sf{}x = 12$

Equation (2) gives

$\sf{}y = 48 - 34$

$\implies \sf{}y = 14$

FINAL ANSWER

Hence Sathwik answered 12 questions right and 14 question wrong.

Hence total number of questions

= 12 + 14 = 26

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