Question

25.
An examination consists of 100 questions. Two marks are awarded for every correct option. One
mark is deducted for every wrong option and half mark is deducted for every question left, then a
person scores 135. Instead, if half mark is deducted for every wrong option and one mark is deducted
for every question left, then the person scores 133. Find the number of questions left unattempted by
the person
(B) 16
(C) 10
(D) 12​

Answer 1

Answer:

c is the correct answer

Answer 2

The number of questions left unattempted by  the person is 14

Solution:

Given that,

An examination consists of 100 questions

Let total number of correct questions be x

Let total number of incorrect questions ne y

Let total number of unanswered questions be z

Then questions left would be {100 - (x + y)}

z = 100 - (x + y)

Two marks are awarded for every correct option. One  mark is deducted for every wrong option and half mark is deducted for every question left, then a  person scores 135

According to this condition,

$2x-y -\frac{z}{2} = 135$

Substitute z = 100 - (x + y)

$2x-y -\frac{100-(x+y)}{2} = 135\\\\4x - 2y - 100 + x - y = 135 \times 2\\\\5x - y = 370------ eqn 1$

Instead, if half mark is deducted for every wrong option and one mark is deducted  for every question left, then the person scores 133

According to this condition,

$2x - \frac{y}{2} - z = 133$

Substitute z = 100 - (x + y)

$2x - \frac{y}{2} - z = 133\\\\2x - \frac{y}{2} - (100-(x+y)) = 133\\\\2x - \frac{y}{2} - 100+x +y = 133\\\\4x - y -200+2x+2y = 133 \times 2\\\\6x +y = 466---- eqn 2$

Solve eqn 1 and eqn 2

Add eqn 1 and eqn 2

5x - y + 6x + y = 370 + 466

11x = 836

Divide both sides by 11

x = 76

Substitute x = 76 in eqn 1

5(76) - y = 370

380 - y = 370

y = 380 - 370

y = 10

y = 10

Find the number of questions left unattempted by  the person

z = 100 - (x + y)

z = 100 - (76 + 10)

z = 100 - 86

z = 14

Thus number of questions left unattempted by  the person is 14

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