The average marks obtained by 150 candidates was 35. If the average marks of passed candidates was 39 and that of the failed candidate was 15, find the number of candidates who passed the examination :

Question

Accepted Answer

To determine the number of candidates who passed the examination, we can use the information provided and apply some basic algebra.

Given:
- Total number of candidates = 150
- Average marks of all candidates = 35
- Average marks of passed candidates = 39
- Average marks of failed candidates = 15

Let $ x $ be the number of candidates who passed the examination. Therefore, the number of candidates who failed is $ 150 - x $.

We can set up the equation based on the total marks:

1. Total marks obtained by all candidates = $ 150 \times 35 = 5250 $
2. Total marks obtained by passed candidates = $ 39x $
3. Total marks obtained by failed candidates = $ 15(150 - x) $

According to the problem, the sum of the marks obtained by passed and failed candidates should equal the total marks obtained by all candidates:

$$ 39x + 15(150 - x) = 5250 $$

Expanding and simplifying the equation:

$$ 39x + 2250 - 15x = 5250 $$

$$ 24x + 2250 = 5250 $$

Subtract 2250 from both sides:

$$ 24x = 3000 $$

Divide by 24:

$$ x = \frac{3000}{24} = 125 $$

Thus, the number of candidates who passed the examination is 125.

Explanation of why Option 2 is correct:
- The calculation shows that 125 candidates passed the examination, which matches Option 2.

Explanation of why other options are incorrect:
- Option 1 (120): If 120 candidates passed, the total marks would not match the given average marks of all candidates.
- Option 3 (135): If 135 candidates passed, the total marks would exceed the given average marks of all candidates.
- Option 4 (140): If 140 candidates passed, the total marks would also exceed the given average marks of all candidates.

Therefore, Option 2 is the only correct answer based on the calculations and given data.