Aman did a 'Mathematics test' in which each correct answer scored 8 marks, and each incorrect answer reduced the score by 4 marks and scored 20 marks. Had 5 marks been awarded for each correct answer and 1 mark been deducted for each incorrect answer, the answer remains the same. How many questions were there in the test?

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answer is D.

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Detailed Solution

Given that the total number of questions =x+y
Marks awarded for x correct answers =8x
Marks reduced for y incorrect answers =4y
Let the number of correct answer =x And the number of incorrect =y

∴

Total number of questions =x+y
In the first case,
Marks awarded for x correct answers =8x
Marks reduced for y incorrect answers =4y
Then

8 x − 4 y = 20 ⇒ 2 x − y = 5 … (i)

In the second case, Marks awarded for x correct answer =5x
Marks reduced for y incorrect answer =y
Then

5 x − y = 20 … (i i)

Subtracting Eq. (i) from Eq. (ii), we have,

3 x = 15 ⇒ x = 5

Then y=5
Thus, the total number of questions are

x + y, i ⋅ e, 5 + 5 = 10

.
Therefore, the total number of questions is 10.
Hence, option (4) is correct.

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