CBSE Class 8 Mathematics Comparing Quantities Assignment Set 09

Percentage

Question 1. A student got 60% of the maximum marks. If the maximum marks is 600. Find his marks.
Answer: Maximum marks = 600
Percentage obtained = \(60\%\)
Marks obtained = \(60\% \text{ of } 600\)
\(= \frac{60}{100} \times 600 = 360\)
In simple words: To find the obtained marks, calculate 60 percent of the total 600 marks.

Exam Tip: Convert the percentage to a fraction or decimal and multiply by the total value.

Question 2. The largest bell in the world weighs 180 tonnes. A bell in Burma weighs 44.5% of it. Find the weight of this ball.
Answer: Weight of the largest bell = 180 tonnes
Percentage of Burma's bell = \(44.5\%\)
Weight of Burma's bell = \(44.5\% \text{ of } 180 \text{ tonnes}\)
\(= \frac{44.5}{100} \times 180\)
\(= \frac{445}{1000} \times 180 = \frac{80100}{1000} = 80.1 \text{ tonnes}\)
In simple words: Multiply 180 by 44.5% to find the weight of the bell in Burma.

Exam Tip: Handle decimals carefully when converting percentages by shifting the decimal point or using fractions.

Question 3. A student got 45 marks out of 75. Express his marks in percentage.
Answer: Marks obtained = 45
Total marks = 75
Percentage = \(\left( \frac{\text{Marks obtained}}{\text{Total marks}} \right) \times 100\%\)
\(= \left( \frac{45}{75} \right) \times 100\%\)
\(= \left( \frac{3}{5} \right) \times 100\% = 3 \times 20\% = 60\%\)
In simple words: Divide the marks obtained by the total marks and multiply by 100 to get the percentage.

Exam Tip: Simplify fractions before multiplying by 100 to make calculations easier.

Question 4. A boy gets \(\frac{1}{3}\) of the maximum marks and fails by 5 marks. If his score is 25, at what percent can he pass?
Answer: Score of the boy = 25
Since he fails by 5 marks, the passing marks = Score + 5 = \(25 + 5 = 30\)
Given that \(\frac{1}{3}\) of the maximum marks is equal to his score (25):
\(\frac{1}{3} \times \text{Maximum marks} = 25\)
Maximum marks = \(25 \times 3 = 75\)
Passing percentage = \(\left( \frac{\text{Passing marks}}{\text{Maximum marks}} \right) \times 100\%\)
\(= \left( \frac{30}{75} \right) \times 100\%\)
\(= \left( \frac{2}{5} \right) \times 100\% = 40\%\)
In simple words: First find the passing marks by adding 5 to his score, then calculate what percentage of the total marks this passing score represents.

Exam Tip: Clearly distinguish between marks scored, passing marks, and maximum marks.

Question 5. A metal contains 70% tin, 25% brass and the rest is zinc. Find the quantity of zinc in 250 kg of this metal.
Answer: Total weight of the metal = 250 kg
Percentage of tin = \(70\%\)
Percentage of brass = \(25\%\)
Percentage of zinc = \(100\% - (70\% + 25\%) = 100\% - 95\% = 5\%\)
Quantity of zinc = \(5\% \text{ of } 250 \text{ kg}\)
\(= \frac{5}{100} \times 250 = \frac{1250}{100} = 12.5 \text{ kg}\)
In simple words: Find the remaining percentage for zinc by subtracting tin and brass percentages from 100%, then calculate that percentage of 250 kg.

Exam Tip: The sum of all percentage parts in a mixture must always equal 100%.

Question 6. In an examination 35% of students failed and 325 students passed. Find the number of students who appeared in the examination.
Answer: Percentage of students failed = \(35\%\)
Percentage of students passed = \(100\% - 35\% = 65\%\)
Let the total number of students who appeared be \(x\).
Given that 65% of total students passed, which equals 325:
\(65\% \text{ of } x = 325\)
\(\frac{65}{100} \times x = 325\)
\(x = \frac{325 \times 100}{65}\)
\(x = 5 \times 100 = 500\)
In simple words: Subtract the failure percentage from 100% to find the passing percentage, then use it to find the total number of students.

Exam Tip: Set up an algebraic equation where the known number of passing students equals their corresponding percentage.

Question 7. You are required to get 40% of maximum marks to pass. But you got 203 marks and declared failed by 27 marks. Find the total number of marks.
Answer: Marks obtained = 203
Marks by which failed = 27
Passing marks = Marks obtained + 27 = \(203 + 27 = 230\)
Given that passing marks is 40% of the maximum marks.
Let the total number of maximum marks be \(x\).
\(40\% \text{ of } x = 230\)
\(\frac{40}{100} \times x = 230\)
\(x = \frac{230 \times 100}{40}\)
\(x = \frac{23000}{40} = 575\)
In simple words: Add the deficit of 27 marks to 203 to get the passing score, and since 40% equals this score, calculate the total maximum marks.

Exam Tip: Always calculate the exact passing threshold before equating it to the passing percentage.

Question 8. I spent 5% of my total income in charity, 22% in business and 53% in family. Now I had Rs 2163 and forty paisa. Find my total income.
Answer: Total percentage spent = \(5\% + 22\% + 53\% = 80\%\)
Percentage of income left = \(100\% - 80\% = 20\%\)
Amount left = Rs 2163.40
Let the total income be \(x\).
\(20\% \text{ of } x = 2163.40\)
\(\frac{20}{100} \times x = 2163.40\)
\(x = \frac{2163.40 \times 100}{20}\)
\(x = \frac{216340}{20} = 10817\)
Total income = Rs 10817
In simple words: Find the percentage of money remaining after all expenses, then use the remaining amount (Rs 2163.40) to calculate the total income.

Exam Tip: Convert forty paisa into decimal form as Rs 0.40 before performing calculations.

Question 9. In an election, a candidate got 60% of the total valid votes. 15% of the total votes were declared invalid. If the total number of votes is 5 Lakhs. Find the number of valid votes polled in favour of the candidate.
Answer: Total number of votes = 5,00,000
Percentage of invalid votes = \(15\%\)
Percentage of valid votes = \(100\% - 15\% = 85\%\)
Total number of valid votes = \(85\% \text{ of } 5,00,000\)
\(= \frac{85}{100} \times 5,00,000 = 85 \times 5000 = 4,25,000\)
Candidate got 60% of the total valid votes.
Number of votes in favour of the candidate = \(60\% \text{ of } 4,25,000\)
\(= \frac{60}{100} \times 4,25,000 = 60 \times 4250 = 2,55,000\)
In simple words: First find the total valid votes by removing the 15% invalid votes, then calculate 60% of those valid votes.

Exam Tip: Percentages of votes are usually calculated out of valid votes unless specified otherwise.

Question 10. In an examination, a student secured 372 marks. If he secured 62% marks find the maximum marks.
Answer: Marks secured = 372
Percentage secured = \(62\%\)
Let the maximum marks be \(x\).
\(62\% \text{ of } x = 372\)
\(\frac{62}{100} \times x = 372\)
\(x = \frac{372 \times 100}{62}\)
Since \(372 \div 62 = 6\):
\(x = 6 \times 100 = 600\)
Maximum marks = 600
In simple words: Set 62 percent of the maximum marks equal to 372 and solve for the total maximum marks.

Exam Tip: Check division shortcuts, as numbers in textbook problems often divide evenly.