Question

50 POINTS!

An examination consists of 160 questions. One mark
is given for every correct option. If one-fourth mark
is deducted for every wrong option and half mark is
deducted for every question left, then one person
scores 79. And if half mark is deducted for every
wrong option and one-fourth mark is deducted for
every left question, the person scores 76, then find
the number of questions he attempted correctly.​

Answer 1

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Answer 2

• Let number for correct questions be M and for wrong questions be N.

• Total number of questions = 160

• And unattempted questions = 160 - (M + N)

☞ CASE 1.

» One mark is given for every correct option. If one-fourth mark is deducted for every wrong option and half mark is deducted for every question left, then one person scores 79.

A.T.Q.

=> 1 × M - $\dfrac{1}{4}$ × N - $\dfrac{1}{2}$ [160 - (M + N)] = 79

=> M - $\dfrac{N}{4}$ - $\dfrac{1}{2}$ (160 - M - N) = 79

=> $\dfrac{4M \: - \: N \: - \: 2(160 \: - \: M \: - \: N)}{4}$ = 79

=> 4M - N - 320 + 2M + 2N = 79 × 4

=> 6M + N - 320 = 316

=> 6M + N = 316 + 320

=> 6M + N = 636

=> N = 636 - 6M ________ (eq 1)

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☞ CASE 2.

» If half mark is deducted for every wrong option and one-fourth mark is deducted for every left question, the person scores 76.

A.T.Q.

=> M - $\dfrac{1}{2}$ N - $\dfrac{1}{4}$ [160 - (M + N)] = 76

=> $\dfrac{4M \: - \: 2N \: - \: (160 \: - \: M \: - \: N)}{4}$ = 76

=> 4M - 2N - 160 + M + N = 76 × 4

=> 5M - N - 160 = 304

=> 5M - N = 304 + 160

=> 5M - N = 464

=> 5M - (636 - 6M) = 464 [From (eq 1)]

=> 5M - 636 + 6M = 464

=> 11M = 464 + 636

=> 11M = 1100

=> M = 100

• Put value of M in (eq 1)

=> N = 636 - 6(11)

=> N = 636 - 600

=> N = 36

Unattempted questions = 160 - (100 + 36)

=> 160 - 136

=> 24

______________________________

He attempted 100 questions correctly.

___________ [ANSWER]

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