Z scored 8 out of 40 in Term I and scored 12 out of 40 in Term 2. If the average Pass percentage is 35% of the average of all Terms, how much should Z score in Term 3 out of 100?  


Let's break down the problem and solve it step by step:

1. **Scores in Term I and Term II:**
   - Z scored 8 out of 40 in Term I.
   - Z scored 12 out of 40 in Term II.

2. **Average score in the first two terms:**
   To calculate the average score percentage in the first two terms:
   \[
   \text{Average Percentage of Term I and II} = \frac{\left(\frac{8}{40} \times 100\right) + \left(\frac{12}{40} \times 100\right)}{2}
   \]
   Let's calculate this:
   \[
   \text{Term I Percentage} = \frac{8}{40} \times 100 = 20\%
   \]
   \[
   \text{Term II Percentage} = \frac{12}{40} \times 100 = 30\%
   \]
   \[
   \text{Average Percentage of Term I and II} = \frac{20 + 30}{2} = 25\%
   \]

3. **Pass percentage requirement:**
   The average Pass percentage required is 35%. This means that after Term III, the overall average percentage should be 35% or more.

4. **Total marks and required marks in Term III:**
   Now, let's assume Z needs to score \( x \) marks out of 100 in Term III.

   The total marks from all three terms would be \( 40 + 40 + 100 = 180 \) marks.

   The formula for the average percentage across all three terms:
   \[
   \text{Average Percentage} = \frac{\left(\frac{8 + 12 + x}{180}\right) \times 100}
   \]

   To pass, Z's average percentage needs to be 35% or more:
   \[
   \frac{20 + 30 + \frac{x}{100} \times 100}{3} \geq 35
   \]
   Simplifying, we get:
   \[
   \frac{50 + x}{3} \geq 35
   \]
   Multiply both sides by 3:
   \[
   50 + x \geq 105
   \]
   Subtract 50 from both sides:
   \[
   x \geq 55
   \]

So, Z needs to score **at least 55 marks out of 100** in Term III to meet the pass percentage.

Would you like more details or have any questions?

Here are five related questions:

1. What is the total percentage score after all three terms if Z scores exactly 55 in Term III?
2. If Z scored 20 in Term I and 30 in Term II, how much would they need to score in Term III to pass?
3. What is the minimum score required in Term III to achieve an average percentage of 40%?
4. How would the required score in Term III change if the pass percentage was 40% instead of 35%?
5. If Term III had only 50 marks, how would Z’s required score change to pass?

**Tip:** When dealing with percentages across multiple tests or terms, always sum the total marks and total scores first, then calculate the percentage to ensure accuracy.

Discover how to calculate the minimum score Z needs in Term 3 to achieve a passing average percentage after scoring 8 out of 40 in Term I and 12 out of 40 in Term II. Understand the percentage and average calculation formulas used in this high school-level math problem.

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