The average marks obtained by Raghav in 15 tests are 25. Zubeida has maintained an average of 23 so far but has taken only 10 of the tests. If each test is out of 30, how much must Zubeida score on average in the remaining 5 tests to still have a chance to match Raghav’s performance?
29
Understanding the Average Marks Problem
The problem asks us to find the average marks Zubeida needs in the remaining tests to match Raghav's overall average across the same total number of tests. To solve this, we first need to figure out the total marks both students achieved or need to achieve.
Calculate Raghav's Total Marks
Raghav took 15 tests and had an average score of 25. The total marks obtained by Raghav is the average score multiplied by the number of tests.
Total Marks (Raghav) = Average Score $\times$ Number of Tests
Total Marks (Raghav) = $25 \times 15$
Total Marks (Raghav) = $375$
So, Raghav scored a total of 375 marks in 15 tests.
Calculate Zubeida's Current Total Marks
Zubeida has taken 10 tests so far and has an average score of 23. Her current total marks are her average score multiplied by the number of tests she has taken.
Current Total Marks (Zubeida) = Current Average Score $\times$ Number of Tests Taken
Current Total Marks (Zubeida) = $23 \times 10$
Current Total Marks (Zubeida) = $230$
Zubeida has scored a total of 230 marks in the first 10 tests.
Determine Zubeida's Target Total Marks
To match Raghav's performance over 15 tests, Zubeida must achieve the same total marks as Raghav in 15 tests. Raghav's total marks over 15 tests were 375.
Target Total Marks (Zubeida) over 15 tests = Total Marks (Raghav) over 15 tests
Target Total Marks (Zubeida) = $375$
Calculate Marks Needed in Remaining Tests
Zubeida needs a total of 375 marks over 15 tests and has already scored 230 in the first 10 tests. The marks she needs in the remaining tests is the target total minus her current total.
Marks Needed in Remaining Tests = Target Total Marks - Current Total Marks
Marks Needed in Remaining Tests = $375 - 230$
Marks Needed in Remaining Tests = $145$
Zubeida needs to score a total of 145 marks in the remaining tests.
Calculate Average Marks Needed in Remaining Tests
There are a total of 15 tests, and Zubeida has taken 10. The number of remaining tests is $15 - 10 = 5$. To find the average score Zubeida needs in these 5 tests, we divide the total marks needed by the number of remaining tests.
Number of Remaining Tests = $15 - 10 = 5$
Average Marks Needed = Marks Needed in Remaining Tests $\div$ Number of Remaining Tests
Average Marks Needed = $145 \div 5$
Average Marks Needed = $29$
Zubeida must score an average of 29 marks in the remaining 5 tests to match Raghav's overall average.
Let's summarize the calculations:
| Calculation | Details | Result |
|---|---|---|
| Raghav's Total Marks | $25 \times 15$ | $375$ |
| Zubeida's Current Total Marks | $23 \times 10$ | $230$ |
| Zubeida's Target Total Marks (to match Raghav) | $375$ | $375$ |
| Marks Needed in Remaining Tests | $375 - 230$ | $145$ |
| Number of Remaining Tests | $15 - 10$ | $5$ |
| Average Marks Needed in Remaining Tests | $145 \div 5$ | $29$ |
Thus, Zubeida must score an average of 29 in the remaining 5 tests.
Revision Table: Average Marks Calculation
Understanding average is key. The average is the total sum divided by the number of items. To find the total sum, you multiply the average by the number of items.
- Average: Sum of values / Number of values
- Sum of values: Average $\times$ Number of values
This problem uses both calculations: finding total scores from averages and then finding a required average from a required total score.
Additional Information: Understanding Averages
An average represents a typical or central value of a set of numbers. It's calculated by summing up all the values in the set and dividing the sum by the count of values in the set.
In this problem, the average test score tells us the score that, if obtained in every test, would result in the same total score as the actual varying scores. For example, Raghav's average of 25 means if he scored exactly 25 in each of the 15 tests, his total would still be 375.
The fact that each test is out of 30 is mentioned but isn't directly used in the calculation of the required average itself, as long as the required average (29) is achievable within the maximum possible score of 30 per test, which it is.
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