CBSE Class 7 Mathematics Comparing Quantities Percentage Assignment Set 01

VII - Mathematics Assignment No - 05 - Comparing Quantities

Percentage (%)

Question Q1. Convert the following percentage into fraction
(a) \(25\%\)
(b) \(12\frac{1}{2}\%\)
(c) \(35\%\)
(d) \(55\%\)
Answer:
(a) \(25\% = \frac{25}{100} = \frac{1}{4}\)
(b) \(12\frac{1}{2}\% = \frac{25}{2}\% = \frac{25}{2 \times 100} = \frac{25}{200} = \frac{1}{8}\)
(c) \(35\% = \frac{35}{100} = \frac{7}{20}\)
(d) \(55\% = \frac{55}{100} = \frac{11}{20}\)
In simple words: To convert a percentage into a fraction, remove the percentage sign and divide the number by 100, then simplify the fraction to its lowest terms.

Exam Tip: Always reduce the resulting fraction to its simplest form by dividing the numerator and denominator by their greatest common divisor.

Question Q2. Convert the following fractions into percentages
(a) \(\frac{3}{5}\)
(b) \(\frac{100}{3}\)
(c) \(\frac{3}{50}\)
(d) \(\frac{25}{2}\)
Answer:
(a) \(\frac{3}{5} = \frac{3}{5} \times 100\% = 3 \times 20\% = 60\%\)
(b) \(\frac{100}{3} = \frac{100}{3} \times 100\% = \frac{10000}{3}\% = 3333\frac{1}{3}\%\)
(c) \(\frac{3}{50} = \frac{3}{50} \times 100\% = 3 \times 2\% = 6\%\)
(d) \(\frac{25}{2} = \frac{25}{2} \times 100\% = 25 \times 50\% = 1250\%\)
In simple words: To convert any fraction into a percentage, multiply the fraction by 100% and simplify.

Exam Tip: Remember to always include the percentage sign (%) at the end of your calculated answer.

Question Q3. Find \(20\%\) of 50
Answer:
\(20\% \text{ of } 50 = \frac{20}{100} \times 50\)
\(= \frac{1}{5} \times 50\)
\(= 10\)
In simple words: To find a percentage of a given number, multiply the number by the percentage written as a fraction or decimal.

Exam Tip: Convert the percentage to a fraction or decimal first to make multiplication and cancellation easier.

Question Q4. What \(\%\) of 15 is 75?
Answer:
Let \(x\%\) of 15 be 75.
\(\frac{x}{100} \times 15 = 75\)
\(x = \frac{75 \times 100}{15}\)
\(x = 5 \times 100\)
\(x = 500\%\)
In simple words: Set up an equation where the unknown percentage of the base number equals the given part, then solve for the percentage.

Exam Tip: The quantity following the word "of" is always the base value placed in the denominator.

Question Q5. What \(\%\) of 4 litres is 300 ml?
Answer:
First, convert both quantities to the same unit (milliliters).
1 litre = 1000 ml
4 litres = \(4 \times 1000 = 4000 \text{ ml}\)
Let the required percentage be \(x\%\).
\(\frac{x}{100} \times 4000 = 300\)
\(40x = 300\)
\(x = \frac{300}{40} = \frac{30}{4} = \frac{15}{2}\%\)
In simple words: Always convert different units into a single common unit before calculating percentages.

Exam Tip: Never calculate percentages directly when units are mismatched (e.g., litres and milliliters).

Question Q6. Find the number whose \(27\%\) is 540.
Answer:
Let the required number be \(x\).
\(27\% \text{ of } x = 540\)
\(\frac{27}{100} \times x = 540\)
\(x = \frac{540 \times 100}{27}\)
\(x = 20 \times 100\)
\(x = 2000\)
In simple words: Assume the unknown number is a variable, set up the percentage equation, and solve for the variable.

Exam Tip: Check your answer by taking 27% of 2000 to see if it yields 540.

Question Q7. A child get 38 marks out of 40. Find his marks in percentage.
Answer:
Percentage of marks = \(\left(\frac{\text{Marks obtained}}{\text{Total marks}} \times 100\right)\%\)
\(= \frac{38}{40} \times 100\%\)
\(= \frac{38}{2} \times 5\%\)
\(= 19 \times 5\%\)
\(= 95\%\)
In simple words: Divide the marks obtained by the total maximum marks and multiply by 100 to get the percentage.

Exam Tip: Marks obtained form the numerator and total maximum marks form the denominator.

Question Q8. Arun's monthly salary is Rs 5000. He saves \(25\%\). Find his expenditure.
Answer:
Monthly salary = Rs 5000
Savings percentage = \(25\%\)
Expenditure percentage = \(100\% - 25\% = 75\%\)
Expenditure = \(75\% \text{ of Rs } 5000\)
\(= \frac{75}{100} \times 5000\)
\(= 75 \times 50\)
\(= \text{Rs } 3750\)
In simple words: Expenditure is what remains after saving. Subtract the savings percentage from 100% to find the expenditure percentage, then calculate the amount.

Exam Tip: Alternatively, calculate savings first (25% of 5000 = Rs 1250) and subtract it from total salary (5000 - 1250 = Rs 3750).

Question Q9. An alloy is made up of \(25\%\) Copper, \(35\%\) nickel and the rest is Zinc. Find the mass of Zinc in 800 kg of the alloy.
Answer:
Total mass of alloy = 800 kg
Percentage of Copper = \(25\%\)
Percentage of Nickel = \(35\%\)
Percentage of Zinc = \(100\% - (25\% + 35\%)\)
\(= 100\% - 60\% = 40\%\)
Mass of Zinc = \(40\% \text{ of } 800 \text{ kg}\)
\(= \frac{40}{100} \times 800\)
\(= 40 \times 8\)
\(= 320 \text{ kg}\)
In simple words: Total percentage of all components in an alloy must equal 100%. Find the remaining percentage for zinc and calculate its mass.

Exam Tip: Ensure the sum of all individual percentages equals 100 before proceeding with calculations.

Question Q10. Anila obtained 650 marks out of 800 and her friend Sunila obtained 450 marks out of 600 in an examination. Whose performance is better?
Answer:
Anila's percentage of marks = \(\frac{650}{800} \times 100\%\)
\(= \frac{650}{8}\% = 81.25\%\)
Sunila's percentage of marks = \(\frac{450}{600} \times 100\%\)
\(= \frac{450}{6}\% = 75\%\)
Comparing the percentages: \(81.25\% > 75\%\)
Therefore, Anila's performance is better.
In simple words: To compare performances with different total marks, convert both scores into percentages and compare the resulting values.

Exam Tip: You cannot compare raw marks directly when total maximum marks are different; percentages provide a common scale.

Question Q11. Convert \(1:2:5\) into \(\%\)
Answer:
Sum of ratio terms = \(1 + 2 + 5 = 8\)
First part percentage = \(\frac{1}{8} \times 100\% = \frac{100}{8}\% = 12\frac{1}{2}\% \text{ (or } 12.5\% \text{)}\)
Second part percentage = \(\frac{2}{8} \times 100\% = \frac{2}{1} \times \frac{100}{8}\% = 25\%\)
Third part percentage = \(\frac{5}{8} \times 100\% = \frac{500}{8}\% = 62\frac{1}{2}\% \text{ (or } 62.5\% \text{)}\)
In simple words: Add all parts of the ratio to get the total denominator, then write each part as a fraction of the total and multiply by 100%.

Exam Tip: Verify your answer by checking if the sum of all calculated percentages equals 100%.

Question Q12. The population of a town in 2008 was 1800000 and in 2009 was 2100000. Find the increase in percentage.
Answer:
Population in 2008 (Initial) = 1800000
Population in 2009 (Final) = 2100000
Increase in population = \(2100000 - 1800000 = 300000\)
Percentage increase = \(\left(\frac{\text{Increase}}{\text{Initial Population}} \times 100\right)\%\)
\(= \frac{300000}{1800000} \times 100\%\)
\(= \frac{3}{18} \times 100\%\)
\(= \frac{1}{6} \times 100\% = \frac{50}{3}\% = 16\frac{2}{3}\%\)
In simple words: Find the absolute increase in value, divide it by the original starting value, and multiply by 100.

Exam Tip: The base for percentage increase or decrease is always the original initial value, never the final value.

Question Q13. After spending \(69\%\) of his monthly earning a man saves Rs 2108. Find his monthly salary.
Answer:
Let the monthly salary be Rs \(x\).
Percentage spent = \(69\%\)
Percentage saved = \(100\% - 69\% = 31\%\)
Given savings = Rs 2108
\(31\% \text{ of } x = 2108\)
\(\frac{31}{100} \times x = 2108\)
\(x = \frac{2108 \times 100}{31}\)
\(x = 68 \times 100 = \text{Rs } 6800\)
In simple words: Calculate the savings percentage first, equate it to the given saving amount, and solve for total earnings.

Exam Tip: Always define your unknown variable clearly at the beginning of the problem.

Question Q14. The reduced price of a fridge after allowing \(10\%\) discount is Rs 11700. Find the original price.
Answer:
Let the original price of the fridge be Rs \(x\).
Discount percentage = \(10\%\)
Reduced price (Selling Price) = \(100\% - 10\% = 90\% \text{ of original price}\)
\(90\% \text{ of } x = 11700\)
\(\frac{90}{100} \times x = 11700\)
\(x = \frac{11700 \times 100}{90}\)
\(x = \frac{1170000}{90} = 13000\)
Original price = Rs 13000
In simple words: The discounted price represents the remaining percentage after subtracting the discount from 100%. Use this to find the original price.

Question Q15. Anil gets 60 marks and fails by 20 marks in an English paper where the maximum marks are 200. Find the pass \(\%\).
Answer:
Marks obtained by Anil = 60
Marks by which he failed = 20
Passing marks = \(60 + 20 = 80\)
Maximum marks = 200
Pass percentage = \(\left(\frac{\text{Passing Marks}}{\text{Maximum Marks}} \times 100\right)\%\)
\(= \frac{80}{200} \times 100\%\)
\(= \frac{80}{2}\% = 40\%\)
In simple words: Add the failing deficit to the marks obtained to find the exact passing marks, then convert that passing score into a percentage.

Exam Tip: Failing by 20 marks means the student needed 20 more marks added to their score to reach the passing threshold.