Several students have taken an exam. There was an error in the answer key which affected the marks of total 48 students, the average marks of these students were reduced from 78 to 66. The average of remaining students increased by 3.5 marks. This resulted the reduction of the average of all students by 4.5 marks. Find the number of students who attended the exam.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 93.
| Understanding | Application |
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Here in this question, we use the alligation method because in the question we have average marks of all students, increment in average marks and decrement in average marks. Let there are total x students in which marks of 48 students decrease from 78 to 66. So the number of remaining students = x - 48 |
Because the total marks is reduced by 4.5 so in alligations we take this as positive so all decrement need to write in positive and all increment need to write in negative
The last value of alligation is nothing but the ratio of the number of students. (48/x - 48) = 8/7.5 48 × 7.5 = (x - 48) × 8 360 = 8x - 384 8x = 360 + 384 8x = 744 x = 93 So, the total number of students is 93. |
