Question : In an examination, the original average mark was found to be 50. To deduct marks for computational errors, the marks of 100 candidates were changed from 90 to 60 each, and the new average of marks became 45. What was the total number of candidates who appeared in the examination?
Option 1: 600
Option 2: 300
Option 3: 200
Option 4: 150
Correct Answer: 600
Solution :
Given: The average of marks = 50
The marks of 100 candidates had to be changed from 90 to 60 each, so the new average = 45
Total marks of 100 candidates before error = 90 × 100 = 9000
Total marks of 100 candidates after error = 60 × 100 = 6000
$\therefore$ The change in marks = 9000 – 6000 = 3000
Let the total number of candidates = 100 + a
Total marks of candidates before error = (100 + a) × 50
Total marks of candidates after error = (100 + a) × 45
According to the given condition,
⇒ 5000 + 50a – 45a – 4500 = 3000
⇒ 500 + 5a = 3000
⇒ 5a = 2500
$\therefore$ a = 500
So, the total students = 500 + 100 = 600
Hence, the correct answer is 600.
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