Question : The average mark obtained by 100 candidates in a certain examination is 30. If the average marks of passed candidates are 35 and those of failed candidates are 10, what is the number of candidates who passed the examination?
Option 1: 60
Option 2: 70
Option 3: 80
Option 4: 90
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Correct Answer: 80
Solution :
Given: The average mark of 100 candidates is 30.
So, total marks = (100 × 30) = 3000
Average marks of passed candidates = 35
Average marks of failed candidates = 10
Let the number of passed candidates be X and the number of failed candidates be Y.
According to the question, (X + Y) = 100 --------------------------(1)
Total marks of passed candidates = 35X
Total marks of failed candidates = 10Y
Total marks = Total marks of passed candidates + Total marks of failed candidates
⇒ 3000 = 35X + 10Y ------------------------------------(2)
Multiplying equation (1) by 10 and subtracting from equation (2),
⇒ (35X + 10Y) – (10X + 10Y) = 3000 – 1000
⇒ 25X = 2000
⇒ X = $\frac{2000}{25}$
⇒ X = 80
Hence, the correct answer is 80.
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