CBSE Class 7 Mathematics Comparing Quantities Profit and Loss Assignment Set 01

VII - Mathematics Assignment No - 07 - Comparing Quantities

Profit And Loss

Question Q1. Arun purchased a scooter for Rs 10,000 and sold it for Rs 12,500. Find his gain percent.
Answer: Cost Price (CP) = Rs 10,000
Selling Price (SP) = Rs 12,500
Gain = SP - CP
Gain = 12500 - 10000 = Rs 2500
Gain % = \(\left(\frac{\text{Gain}}{\text{CP}}\right) \times 100\)
Gain % = \(\left(\frac{2500}{10000}\right) \times 100 = 25\%\)
In simple words: Arun made a profit of Rs 2500 on his scooter, which is 25 percent of the original price.

Exam Tip: Always calculate profit or loss percentage on the Cost Price unless specified otherwise.

Question Q2. There are 60 students in a class, out of which 25 are girls. Find the percentage of boys in the class.
Answer: Total number of students = 60
Number of girls = 25
Number of boys = 60 - 25 = 35
Percentage of boys = \(\left(\frac{\text{Number of boys}}{\text{Total students}}\right) \times 100\)
Percentage of boys = \(\left(\frac{35}{60}\right) \times 100 = \frac{175}{3} = 58\frac{1}{3}\%\)
In simple words: First find the number of boys by subtracting girls from total students, then convert that into a percentage.

Exam Tip: Make sure to find the required quantity (boys, not girls) before calculating the percentage.

Question Q3. Convert the following into percentage: (a) \(\frac{1}{3}\) (b) \(0.05\) (c) \(4.5\)
Answer: (a) \(\frac{1}{3} \times 100 = \frac{100}{3}\% = 33\frac{1}{3}\%\)
(b) \(0.05 \times 100 = 5\%\)
(c) \(4.5 \times 100 = 455\%\) (Correction: \(4.5 \times 100 = 450\%\) based on standard math, but looking at answer key given as 45%, let us check: \(0.45 \times 100 = 45%\). As per handwritten sheet it is written as 4.5, multiplying by 100 gives 450% or as per answer key 45%. Let's write standard conversion: \(4.5 \times 100 = 450\%\)).
In simple words: To convert any fraction or decimal into a percentage, simply multiply it by 100.

Exam Tip: Shift the decimal point two places to the right when multiplying a decimal number by 100.

Question Q4. A person saves Rs 500 from his salary. If this is 20% of his salary, find his salary.
Answer: Let the total salary be Rs \(x\).
Given, 20% of salary = Rs 500
\(\frac{20}{100} \times x = 500\)
\(x = \frac{500 \times 100}{20}\)
\(x = 500 \times 5 = 2500\)
Total salary = Rs 2500
In simple words: Set up an equation where 20 percent of the unknown total equals 500, then solve for the total.

Exam Tip: Translate "percentage of a quantity" directly into a multiplication equation with a variable.

Question Q5. Find the whole quantity if (a) \(33\frac{1}{3}\%\) of it is 500 (b) \(12\%\) of it is 96
Answer: (a) Let the whole quantity be \(x\).
\(33\frac{1}{3}\% \text{ of } x = 500\)
\(\frac{100}{3}\% \text{ of } x = 500\)
\(\frac{100}{300} \times x = 500 \implies \frac{1}{3} \times x = 500\)
\(x = 500 \times 3 = 1500\) (Note: answer key lists 15 based on direct unit factor, but full quantity is 1500).
(b) Let the whole quantity be \(y\).
\(12\% \text{ of } y = 96\)
\(\frac{12}{100} \times y = 96\)
\(y = \frac{96 \times 100}{12} = 8 \times 100 = 800\)
In simple words: Divide the given part by the percentage value and multiply by 100 to find the whole quantity.

Exam Tip: Convert mixed fractions into improper fractions before setting up the equation.

Question Q6. If angles of a triangle are in the ratio 1 : 3 : 5. Find each angle.
Answer: Let the angles be \(1x\), \(3x\), and \(5x\).
We know that the sum of all angles in a triangle is \(180^\circ\).
\(1x + 3x + 5x = 180^\circ\)
\(9x = 180^\circ\)
\(x = \frac{180^\circ}{9} = 20^\circ\)
First angle = \(1 \times 20^\circ = 20^\circ\)
Second angle = \(3 \times 20^\circ = 60^\circ\)
Third angle = \(5 \times 20^\circ = 100^\circ\)
In simple words: Use the ratio parts with a variable \(x\), equate their sum to 180 degrees, find \(x\), and multiply it by each ratio term.

Exam Tip: Always verify your answer by adding the calculated angles to check if their sum is exactly \(180^\circ\).

Question Q7. The population of a town decreased from 30,000 to 25,000. Find the percentage decrease.
Answer: Initial population = 30,000
Final population = 25,000
Decrease in population = 30000 - 25000 = 5000
Percentage decrease = \(\left(\frac{\text{Decrease}}{\text{Initial Population}}\right) \times 100\)
Percentage decrease = \(\left(\frac{5000}{30000}\right) \times 100 = \frac{500}{3}\% = 16\frac{2}{3}\%\)
In simple words: Find the drop in population, divide it by the starting population, and multiply by 100.

Exam Tip: The denominator for percentage increase or decrease is always the original initial value.

Question Q8. In a sale, a person reduces the price of an article by 15%. If the reduced price of the article is Rs 3400, find his original price.
Answer: Let the original price be Rs \(x\).
The price is reduced by 15%, so the new price is \(100\% - 15\% = 85\%\) of the original price.
\(85\% \text{ of } x = 3400\)
\(\frac{85}{100} \times x = 3400\)
\(x = \frac{3400 \times 100}{85}\)
\(x = \frac{340000}{85} = 4000\)
Original price = Rs 4000
In simple words: Since 15 percent was taken off, the new price is 85 percent of the original. Solve for 100 percent.

Exam Tip: When a quantity is reduced by \(p\%\), the remaining percentage is \((100 - p)\%\).

Question Q9. In an examination, a student must get 40% marks to pass. A student gets 48 marks out of 200. Express his marks as a percentage. How many more marks should he have got to pass the examination?
Answer: Total maximum marks = 200
Marks obtained by student = 48
Percentage of marks obtained = \(\left(\frac{48}{200}\right) \times 100 = 24\%\)
Passing marks percentage = 40%
Passing marks required = \(40\% \text{ of } 200 = \frac{40}{100} \times 200 = 80\)
More marks required to pass = Passing marks - Marks obtained
More marks required = 80 - 48 = 32 marks
In simple words: First find the student's percentage, then calculate the passing marks out of 200 and find the difference.

Question Q10. Sunita sold a bangle for Rs 4500 and lost 10%. For how much should she have sold it to gain 20%?
Answer: Selling Price (SP1) = Rs 4500
Loss % = 10%
Cost Price (CP) = \(\frac{\text{SP1} \times 100}{100 - \text{Loss}\%}\)
CP = \(\frac{4500 \times 100}{100 - 10} = \frac{4500 \times 100}{90} = 5000\)
Cost Price of the bangle = Rs 5000
Now, desired Gain % = 20%
New Selling Price (SP2) = \(\text{CP} \times \left(\frac{100 + \text{Gain}\%}{100}\right)\)
SP2 = \(5000 \times \left(\frac{100 + 20}{100}\right) = 5000 \times \frac{120}{100} = 50 \times 120 = 6000\)
New Selling Price = Rs 6000
In simple words: First find the original cost price using the loss formula, then calculate the new selling price for a 20 percent profit.

Exam Tip: Always find the Cost Price first whenever you need to switch between different profit and loss scenarios.