Adithya got 78% marks in the examination. If he secured 663 marks, find the maximum marks.
850
Let's figure out the maximum marks Adithya could have gotten in the examination. We know Adithya scored 78% marks, and this score corresponds to 663 marks.
We need to find the total possible marks, which we call the maximum marks. We can set up a simple equation using percentages.
Calculating Maximum Marks from Percentage
If we let the maximum marks be represented by $M$, then 78% of $M$ is equal to 663 marks. We can write this mathematically:
\( 78\% \text{ of } M = 663 \)
To work with this equation, we need to convert the percentage to a decimal or a fraction. Remember that a percentage means 'out of 100'. So, 78% is the same as \(\frac{78}{100}\) or 0.78.
Using the decimal form, the equation becomes:
\( 0.78 \times M = 663 \)
To find the value of \(M\), we need to isolate \(M\) on one side of the equation. We can do this by dividing both sides of the equation by 0.78:
\( M = \frac{663}{0.78} \)
Now, let's perform the division:
\( M = \frac{663}{0.78} = \frac{663 \times 100}{0.78 \times 100} = \frac{66300}{78} \)
We can perform this division to find the value of \(M\).
\( \frac{66300}{78} \)
| Step | Calculation | Explanation |
|---|---|---|
| 1 | Divide 663 by 78 | $663 \div 78$. $78 \times 8 = 624$. Remainder $663 - 624 = 39$. Bring down the next digit (0). |
| 2 | Divide 390 by 78 | $390 \div 78$. $78 \times 5 = 390$. Remainder $390 - 390 = 0$. Bring down the last digit (0). |
| 3 | Divide 0 by 78 | $0 \div 78 = 0$. |
| Result | 850 | The quotient is 850. |
So, the maximum marks \(M\) is 850.
Therefore, the maximum marks for the examination were 850.
Revision Table: Percentage Calculations
| Concept | Explanation | Example |
|---|---|---|
| Percentage Definition | A rate, number, or amount in each hundred. Represented by the symbol %. | 10% means 10 out of 100. |
| Converting Percentage to Decimal | Divide the percentage by 100. | $78\% = \frac{78}{100} = 0.78$ |
| Calculating Percentage of a Number | Convert the percentage to a decimal or fraction and multiply by the number. | $20\%$ of 50: $0.20 \times 50 = 10$. Or $\frac{20}{100} \times 50 = 10$. |
| Finding the Whole from a Percentage | If $P\%$ of $W$ is $X$, then $W = \frac{X}{P\%} = \frac{X}{(P/100)} = \frac{X \times 100}{P}$. | If 78% of $W$ is 663, $W = \frac{663 \times 100}{78} = 850$. |
Additional Information on Percentages
Percentages are a common way to express a part of a whole in terms of 100. They are used in many real-life situations, like calculating discounts, interest rates, test scores, and statistics.
- To calculate the percentage of marks obtained in an exam, you divide the marks obtained by the maximum marks and multiply by 100.
- In this problem, we did the reverse: we knew the percentage and the part (marks obtained) and needed to find the whole (maximum marks).
- Understanding how to convert between percentages, decimals, and fractions is crucial for solving percentage-based problems.
By setting up the equation correctly, we were able to find the total maximum marks Adithya's examination was out of.
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