Question
In a class test (+3) marks are given for every correct answer and (−2) marks are given for every incorrect answer and no marks for not attempting a question. Rakesh scores 18 marks by attempting 16 questions. How many questions has he attempted correctly and how many has he attempted incorrectly? [4 MARKS]
Answer:
:
Writing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Marks obtained for 1 right answer = +3
Marks obtained for 1 wrong answer = −2
Total marks scored by Rakesh = 18
Number of questions attempted = 16
(No. of correct ans)(3) + (No. of incorrect ans)(-2)
= 18
⇒ (No. of correct ans)(3) + (16 - No. of correct ans)(-2)
= 18
⇒ (No. of correct ans)(3) + -32 + 2(No. of correct ans)
= 18
⇒ (No. of correct ans)(5) + -32 = 18
⇒ (No. of correct ans)(5) = 18 + 32 = 50
⇒ No. of correct ans = 10
∴ No. of incorrect ans = 16 - 10 = 6
∴ Total number of correct and incorrect answers scored by Rakesh is 10 and 6 respectively.
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:
Writing the equation: 1 Mark
Steps: 2 Marks
Result: 1 Mark
Marks obtained for 1 right answer = +3
Marks obtained for 1 wrong answer = −2
Total marks scored by Rakesh = 18
Number of questions attempted = 16
(No. of correct ans)(3) + (No. of incorrect ans)(-2)
= 18
⇒ (No. of correct ans)(3) + (16 - No. of correct ans)(-2)
= 18
⇒ (No. of correct ans)(3) + -32 + 2(No. of correct ans)
= 18
⇒ (No. of correct ans)(5) + -32 = 18
⇒ (No. of correct ans)(5) = 18 + 32 = 50
⇒ No. of correct ans = 10
∴ No. of incorrect ans = 16 - 10 = 6
∴ Total number of correct and incorrect answers scored by Rakesh is 10 and 6 respectively.
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