The ABS school organised Science competition for seventh class students. In this exam, there were 40 questions, all MCQ types. Three marks were awarded for each correct answer and one mark was deducted for each question that was answered incorrectly or left unanswered.
(1) Aryan scored 76 marks. How many questions did he answer correctly ?
23
25
7
29
(2) Ramya scored 84 marks. If she attempted all the questions, how many of her answers were incorrect ?
9
10
11
12
(3) Hema's score was double the number of questions she attempted correctly. How many of her answers were correct ?
10
15
20
25
(4) Bilok's score was the highest in the class. His score was 12 marks less than the maximum marks. How many of his answers were correct ?
35
36
37
38
Linear Eqns One Variable
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Question

The ABS school organised Science competition for seventh class students. In this exam, there were 40 questions, all MCQ types. Three marks were awarded for each correct answer and one mark was deducted for each question that was answered incorrectly or left unanswered.
(1) Aryan scored 76 marks. How many questions did he answer correctly ?
23
25
7
29
(2) Ramya scored 84 marks. If she attempted all the questions, how many of her answers were incorrect ?
9
10
11
12
(3) Hema's score was double the number of questions she attempted correctly. How many of her answers were correct ?
10
15
20
25
(4) Bilok's score was the highest in the class. His score was 12 marks less than the maximum marks. How many of his answers were correct ?
35
36
37
38

Linear Eqns One Variable

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KnowledgeBoat · Accepted Answer

Given: Total Questions: 40 Correct Answer: +3 marks Incorrect/Unanswered: -1 mark Let c = correct answers. Then (40 - c) = incorrect/unanswered. (1) Aryan scores 76 marks: 3(c) - 1(40 - c) = 76 ⇒ 3c - 40 + c = 76 ⇒ 4c - 40 = 76 ⇒ 4c = 76 + 40 [Transposing -40 to RHS] ⇒ 4c = 116 ⇒ c = ⇒ c = 29 Aryan answered 29 questions correctly. Hence, option 4 is the correct option. (2) Ramya scored 84 marks: 3(c) - 1(40 - c) = 84 ⇒ 3c - 40 + c = 84 ⇒ 4c - 40 = 84 ⇒ 4c = 84 + 40 [Transposing -40 to RHS] ⇒ 4c = 124 ⇒ c = ⇒ c = 31 Correct answers = 31 Incorrect answers = (40 - c) = (40 - 31) = 9. Hence, option 1 is the correct option. (3) Hema's score was double the number of questions she attempted correctly: Score = 2c 3c - (40 - c) = 2c ⇒ 3c - 40 + c = 2c ⇒ 4c - 40 = 2c ⇒ 4c - 2c = 40 [Transposing +2c to LHS and -40 to RHS] ⇒ 2c = 40 ⇒ c = ⇒ c = 20 Hema answered 20 questions correctly. Hence, option 3 is the correct option. (4) Bilok's score was 12 marks less than the maximum marks Maximum possible marks = 40 x 3 = 120. Bilok's score = 120 - 12 = 108. 3c - (40 - c) = 108 ⇒ 3c - 40 + c = 108 ⇒ 4c - 40 = 108 ⇒ 4c = 108 + 40 [Transposing -40 to RHS] ⇒ 4c = 148 ⇒ c = ⇒ c = 37 Bilok answered 37 questions correctly. Hence, option 3 is the correct option.

Mathematics

Linear Eqns One Variable

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