A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% in the test and all questions carried equal marks, then what is the number of questions in the test ?

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Q: 146 (IAS/2010)
A candidate attempted 12 questions and secured full marks in all of them. If he obtained 60% in the test and all questions carried equal marks, then what is the number of questions in the test ?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,11,9,1,3,5,11

keywords: 

{'equal marks': [0, 0, 2, 0], 'questions': [2, 0, 5, 3], 'test': [2, 2, 8, 3], 'full marks': [0, 0, 2, 0], 'number': [0, 0, 0, 2], 'candidate': [1, 0, 0, 0]}

Let the total number of questions in the test be x. As the candidate attempted 12 questions, he left out (x - 12) questions.

As he secured full marks in all 12 questions attempted, his total score from these questions is 12 (assuming each question carries 1 mark).

Let the marks for each question be m. Then, the total marks in the test is x m.

As the candidate obtained 60% in the test, his total score is 0.6 times the total marks in the test. Therefore, we can write:

12m + (x - 12) * 0 = 0.6 * xm

Simplifying this equation, we get:

12m = 0.6xm

Dividing both sides by 0.6m, we get:

20 = x

Therefore, the total number of questions in the test is 20. The correct answer is option (D) 20.

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