Calculating Chemistry Marks for Target Average

This problem requires us to find the score needed in a third subject (Chemistry) to achieve a specific average score across three subjects, given the scores in the other two.

Understanding the Problem

We are given:

• Marks in Mathematics: 75
• Marks in Physics: 85
• Desired Average Marks (for Math, Physics, and Chemistry): 80
• Number of subjects: 3

We need to find the marks required in Chemistry.

Average Calculation Explained

The average of a set of numbers is calculated by dividing the sum of the numbers by the count of the numbers.

The formula for the average is:

$ \text{Average} = \frac{\text{Sum of Marks}}{\text{Number of Subjects}} $

Step-by-Step Solution

Let the marks obtained by Raju in Chemistry be represented by '$C$'.

1. Set up the average equation: We want the average of the marks in Mathematics, Physics, and Chemistry to be 80. $ \frac{75 + 85 + C}{3} = 80 $
2. Calculate the total marks needed: To achieve an average of 80 over 3 subjects, the total marks required are: $ \text{Total Marks} = \text{Desired Average} \times \text{Number of Subjects} $ $ \text{Total Marks} = 80 \times 3 = 240 $
3. Calculate the sum of known marks: Find the sum of marks Raju already has in Mathematics and Physics. $ \text{Sum of known marks} = 75 + 85 = 160 $
4. Calculate the required Chemistry marks: Subtract the sum of known marks from the total marks needed to find the marks required in Chemistry. $ C = \text{Total Marks needed} - \text{Sum of known marks} $ $ C = 240 - 160 $ $ C = 80 $

Conclusion

Raju must obtain 80 marks in Chemistry to achieve an average score of 80 marks in all three subjects.

Verification

Let's check if an average of 80 is achieved with 80 marks in Chemistry:

$ \text{Average} = \frac{75 + 85 + 80}{3} = \frac{240}{3} = 80 $

The calculation is correct.