If, in a competitive exam, the marks obtained by Sam are 19% less than those of Peter, then the marks obtained by Peter are how much percentage more than the marks obtained by Sam? (Correct to two decimal places)
23.46%
Calculating Percentage Difference in Competitive Exam Marks
This problem asks us to find the percentage by which Peter's marks are more than Sam's marks, given that Sam's marks are 19% less than Peter's marks in a competitive exam.
Understanding the Relationship Between the Marks
Let's denote Peter's marks by \(P\) and Sam's marks by \(S\).
We are told that Sam's marks are 19% less than Peter's marks. This means Sam's marks are equal to Peter's marks minus 19% of Peter's marks.
We can write this relationship mathematically:
\(S = P - 19\%\) of \(P\)
\(S = P - \frac{19}{100} \times P\)
\(S = P - 0.19P\)
\(S = (1 - 0.19)P\)
\(S = 0.81P\)
This equation tells us that Sam's marks are 0.81 times Peter's marks.
Calculating the Percentage More
Now, we want to find by what percentage Peter's marks (\(P\)) are more than Sam's marks (\(S\)). To do this, we need to find the difference between their marks (\(P - S\)) and express this difference as a percentage of Sam's marks (\(S\)), because we are comparing Peter's marks to Sam's marks.
The formula for percentage increase is:
\(\text{Percentage Increase} = \frac{\text{Difference}}{\text{Base Value}} \times 100\%\)
Here, the Difference is \(P - S\), and the Base Value is \(S\).
\(\text{Percentage More} = \frac{P - S}{S} \times 100\%\)
We know that \(S = 0.81P\). We can substitute this into the formula:
\(\text{Percentage More} = \frac{P - 0.81P}{0.81P} \times 100\%\)
\(\text{Percentage More} = \frac{(1 - 0.81)P}{0.81P} \times 100\%\)
\(\text{Percentage More} = \frac{0.19P}{0.81P} \times 100\%\)
We can cancel out \(P\) from the numerator and the denominator:
\(\text{Percentage More} = \frac{0.19}{0.81} \times 100\%\)
\(\text{Percentage More} = \frac{19}{81} \times 100\%\)
\(\text{Percentage More} = \frac{1900}{81}\%\)
Performing the Calculation and Rounding
Now, we calculate the numerical value:
\(\frac{1900}{81} \approx 23.45679...\%\)
The question asks for the answer correct to two decimal places. We look at the third decimal place, which is 6. Since 6 is 5 or greater, we round up the second decimal place.
\(23.45679...\% \approx 23.46\%\)
So, the marks obtained by Peter are approximately 23.46% more than the marks obtained by Sam.
Revision Table: Key Percentage Formulas
| Concept | Formula | Notes |
|---|---|---|
| Percentage Change | \(\frac{\text{Change}}{\text{Original Value}} \times 100\%\) | Change = New Value - Original Value |
| Value After % Decrease | Original Value \(\times\) \((1 - \frac{\text{% Decrease}}{100})\) | Example: 20% decrease from 100 is \(100 \times (1 - 0.20) = 80\). |
| Value After % Increase | Original Value \(\times\) \((1 + \frac{\text{% Increase}}{100})\) | Example: 20% increase from 100 is \(100 \times (1 + 0.20) = 120\). |
| Finding Original Value from % Decrease | New Value / \((1 - \frac{\text{% Decrease}}{100})\) | If 80 is 20% less than Original, Original = \(80 / (1 - 0.20) = 80 / 0.80 = 100\). |
Additional Information on Percentage Calculations
- Percentage problems often require careful reading to identify the correct base value for the calculation. In this problem, the base changes from Peter's marks (for Sam's decrease) to Sam's marks (for Peter's increase).
- A percentage decrease from value A to value B will result in a different percentage increase from value B to value A, unless the percentage change is 0%.
- These types of questions test your understanding of relative change. They are common in aptitude tests and competitive exams.
- Practicing with different percentage values will help solidify the concept and speed up calculation in exams.
Similar Questions
In an election between three candidates, Arjun, Bhaskar and Saral contested for a post. Arjun got 50% votes more than Saral, and Saral got 2% votes less than Bhaskar. The difference between the votes of Bhaskar and Saral is 1296. What is the half of the difference between the votes of Arjun and Bhaskar?
If x% of 280 = 15% of 240 + 20% of 310, then the value of x is:
If the side of an equilateral triangle is increased by 34%, then by what percentage will its area increase?
If the price of petrol increased by 7%, then by what percentage should the consumption be decreased by the consumer, if the expenditure on petrol remains unchanged?
Pass percentage of an examination is 35%. If a student who get 210 marks, failed by 14 marks, then what are the maximum marks of the examination?
In an examination a candidate had to sit for three papers A, B, and C. The candidate secured 75% marks in Paper A, 80% marks in Paper B, and 60% marks in Paper C. If the weightage assigned to Papers A, B, and C were 40%, 50% and 10%, respectively, then find the weighted percentage of marks obtained by the candidate, when all the three papers were taken together.
Tarun owned a plot of land having an area that was 10% more than the area of the plot owned by Basab, while the area of the plot of land owned by Nakul was 40% more than the area of the plot owned by Tarun. If the area of the plot owned by Nakul was 2695 square feet, what was the area (in square feet) of the plot owned by Basab?
A father gives 8% of his monthly income to both his sons as pocket money. The elder son gets 85% of the total amount given to both sons. He spends 90% of the amount and saves Rs. 17. What is the monthly income of his father?
Soham’s initial expenditure and savings were in the ratio of 5 ∶ 3. His income increases by 25%. If his initial savings were ₹4,500, find his income (in ₹) after the increment.
Ram loses 12 \(\frac{1}{2}\) % of his money and after spending 75% of the remainder, is left with Rs. 630. How much money did Ram have initially?
Important Questions from Percentage
A number p increased by p% of 99 equals 99 increased by 99% of p. What is (p + 51)% of 928 + 72?
Amina saves 16% of her income. Now her income is increased by 20% but she still saves the same amount as before. What is the percentage increase in her expenditure?
What is 12% of 4% of 7% of 2 × 10 6 ?
Vignesh spends 42% of his monthly salary on food, 16% on house rent, 11% on entertainment and 7% on conveyance. But due to some family function, he has to borrow Rs. 12,000 from a money leader to meet the expenses of Rs. 18,000 What is his monthly salary?
If X is 12.25% more than Y. then Y is approximately_____ less than X.
