| Directions: Q. 6 to 10 | ||
| A test consists of 'True' or 'False' questions. One mark is awarded for every correct answer while \[\frac{1}{4}\] mark is deducted for every wrong answer. | ||
| A student knew answers to some of the questions. Rest of the questions he attempted by guessing. He answered 120 questions and got 90 marks. | ||
| Type Question | Marks given for correct answer | Marks deducted for wrong answer |
| True/False | 1 | 0.25 |
A) 96
B) 92
C) 90
D) None of these
Correct Answer: A
Solution :
| Let the number of questions whose answer is known to the student be x and questions attempted by guessing be y. |
| Then, x+y=120 ...(i) |
| and \[x-\frac{1}{4}y=90\] |
| \[\Rightarrow \,\,\,\,\,\,4x-y=360\] … (ii) |
| On adding Eqs. (i) and (ii), we get |
| \[5x=480\] |
| \[\Rightarrow x=\frac{480}{5}=96\] |
| Put x = 96 in Eq. (i), we get |
| \[96+y=120\Rightarrow y=120-96=24\] |
| He answered 96 questions correctly. |
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