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The average of marks obtained by 76 candidates in a certain examination is 32. If the average score of passed candidates is 40 and that of the failed candidates is 2, what is the number of candidates who failed the examination?  Ops:   A. 7    B. 9    C. 12    D. 16

Question

The average of marks obtained by 76 candidates in a certain examination is 32. If the average score of passed candidates is 40 and that of the failed candidates is 2, what is the number of candidates who failed the examination?  Ops:   A. 7    B. 9    C. 12    D. 16

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Solution

Let's solve this step by step:

Step 1: We know that the total marks of all candidates is the average mark times the number of candidates. So, the total marks of all candidates is 76 * 32 = 2432.

Step 2: Let's assume the number of passed candidates is P and the number of failed candidates is F. We know that P + F = 76.

Step 3: We also know that the total marks of all candidates is the sum of the total marks of passed candidates and failed candidates. So, 2432 = 40P + 2F.

Step 4: We can express F in terms of P from step 2: F = 76 - P.

Step 5: Substitute F in the equation from step 3: 2432 = 40P + 2(76 - P).

Step 6: Simplify the equation: 2432 = 40P + 152 - 2P.

Step 7: Combine like terms: 2432 = 38P + 152.

Step 8: Subtract 152 from both sides: 2280 = 38P.

Step 9: Divide both sides by 38 to solve for P: P = 60.

Step 10: Substitute P = 60 in the equation from step 4 to find F: F = 76 - 60 = 16.

So, the number of candidates who failed the examination is 16 (Option D).

This problem has been solved

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