Question
How many students appeared in at most two
exams? Study the following information carefully and answer the given questions: There are 1000 students in a college. Out of 1000 students some appeared in exams ‘X’, ‘Y’ and ‘Z’ while some not. Number of student not appeared in any exam is equal to number of students appeared in exam ‘Z’ only. Number of students appeared in exam ‘Y’ is 360. Ratio of number of students appeared in exam ‘X’ and ‘Y’ only to number of students appeared in exam ‘Y’ and ‘Z’ only is 2:3. Number of student appeared in exam ‘X’ and ‘Z’ both is half of number of students appeared in only exam ‘Z’. Number of students appeared in exam ‘X’ only is 50% more than number of students appeared in ‘Y’ only. Number of students appeared in all the three exam is 4% of the total number of students in the college. Number of students appeared in ‘Y’ exam only is same as number of students appeared in ‘Y’ and ‘Z’ only.Solution
Total students = 1000 Let, students appear in exam Z only = a Total students appeared in exam Y = 360 Ratio of number of students appeared in exam X and Y only to students appeared in exam Y and Z only = 2:3 Students appeared in exam X and Z both = a/2 Number of students appeared in all three exams = (4/100) × 1000 = 40 Number of students appeared in Y exam only = No. of students appeared in Y and Z only = 3x Number of students appeared in exam X and Y only = (2/3) × 3x = 2x Now, 2x + 3x + 3x + 40 = 360 ⇒ x = 40 And, 12.5x + a + a/2 + a = 1000 => 5a/2 = 500 ⇒ a = 200 
Students appeared in atmost two exams = 180 + 120 + 200 + 60 + 80 + 120 + 200 = 960
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