GSEB Class 7 Maths Solutions Chapter 8 રાશિઓની તુલના Exercise 8.3

Gujarat Board Textbook Solutions Class 7 Maths Chapter 8 રાશિઓની તુલના Ex 8.3

Question 1. From the following statements, find the profit or loss. Also, find the profit percentage and loss percentage.
(a) A scissor used in the garden was bought for Rs 250 and sold for Rs 325.
Answer: Here, the cost price of the scissor \( = \text{Rs } 250 \). The selling price of the scissor \( = \text{Rs } 325 \). Since \( 325 > 250 \), there is a profit on the sale of the scissor. Profit \( = \) Selling Price \( - \) Cost Price \( = 325 - 250 = \text{Rs } 75 \). The profit percentage \( = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{75}{250} \times 100 = 30\% \). Thus, there is a 30% profit on the sale of the scissor.
In simple words: The scissors were bought for Rs 250 and sold for Rs 325, making a profit of Rs 75. This means there was a 30% profit on the sale.

Exam Tip: Remember that profit or loss percentage is always calculated based on the cost price of the item.

Question 1. (b) A refrigerator was bought for Rs 12,000 and sold for Rs 13,500.
Answer: Here, the cost price of the refrigerator \( = \text{Rs } 12,000 \). The selling price of the refrigerator \( = \text{Rs } 13,500 \). Since \( 13,500 > 12,000 \), there is a profit on the sale of the refrigerator. Profit \( = \) Selling Price \( - \) Cost Price \( = 13,500 - 12,000 = \text{Rs } 1500 \). The profit percentage \( = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{1500}{12000} \times 100 = \frac{150}{12} = 12.5\% \).
In simple words: The fridge was purchased for Rs 12,000 and later sold for Rs 13,500. This resulted in a Rs 1500 profit, which is a 12.5% gain.

Exam Tip: Always double-check calculations when dealing with larger numbers to avoid errors in profit or loss figures and percentages.

Question 1. (c) A cupboard was bought for Rs 2500 and sold for Rs 3000.
Answer: Here, the cost price of the cupboard \( = \text{Rs } 2500 \). The selling price of the cupboard \( = \text{Rs } 3000 \). Since \( 3000 > 2500 \), there is a profit on the sale of the cupboard. Profit \( = \) Selling Price \( - \) Cost Price \( = 3000 - 2500 = \text{Rs } 500 \). The profit percentage \( = \frac{\text{Profit}}{\text{Cost Price}} \times 100 = \frac{500}{2500} \times 100 = 20\% \). Thus, there is a 20% profit on the sale of the cupboard.
In simple words: A cupboard was bought for Rs 2500 and sold for Rs 3000. This made a profit of Rs 500, which is a 20% profit.

Exam Tip: Clearly identify the cost price and selling price before calculating profit or loss to ensure the correct values are used.

Question 1. (d) A skirt's cost price is Rs 250 and it was sold for Rs 150.
Answer: Here, the cost price of the skirt \( = \text{Rs } 250 \). The selling price of the skirt \( = \text{Rs } 150 \). Since \( 150 < 250 \), there is a loss on the sale of the skirt. Loss \( = \) Cost Price \( - \) Selling Price \( = 250 - 150 = \text{Rs } 100 \). The loss percentage \( = \frac{\text{Loss}}{\text{Cost Price}} \times 100 = \frac{100}{250} \times 100 = 40\% \).
In simple words: The skirt was bought for Rs 250 but sold for Rs 150. This means there was a loss of Rs 100, which is a 40% loss.

Exam Tip: When the selling price is less than the cost price, it indicates a loss, and the loss percentage formula should be used correctly.

Question 2. Convert the terms of the following ratios into percentages:
(a) 3:1
Answer: The given ratio \( = 3 : 1 \). The sum of the terms of the ratio \( = 3 + 1 = 4 \). The first term as a percentage \( = \left( \frac{3}{4} \times 100 \right)\% = 75\% \). The second term as a percentage \( = \left( \frac{1}{4} \times 100 \right)\% = 25\% \).
In simple words: For the ratio 3:1, the total parts are 4. The first part is 75% of the total, and the second part is 25%.

Exam Tip: To convert a ratio to percentages, first find the sum of the ratio terms, then divide each term by the sum and multiply by 100.

Question 2. (b) 2:3:5
Answer: The given ratio \( = 2 : 3 : 5 \). The sum of the terms of the ratio \( = 2 + 3 + 5 = 10 \). The first term as a percentage \( = \left( \frac{2}{10} \times 100 \right)\% = 20\% \). The second term as a percentage \( = \left( \frac{3}{10} \times 100 \right)\% = 30\% \). The third term as a percentage \( = \left( \frac{5}{10} \times 100 \right)\% = 50\% \).
In simple words: For the ratio 2:3:5, the total parts are 10. The parts represent 20%, 30%, and 50% respectively.

Exam Tip: Always ensure that the sum of the calculated percentages equals 100% to verify your answer for ratio to percentage conversions.

Question 2. (c) 1:4
Answer: The given ratio \( = 1 : 4 \). The sum of the terms of the ratio \( = 1 + 4 = 5 \). The first term as a percentage \( = \left( \frac{1}{5} \times 100 \right)\% = 20\% \). The second term as a percentage \( = \left( \frac{4}{5} \times 100 \right)\% = 80\% \).
In simple words: In the ratio 1:4, the total is 5 parts. This means the first part is 20% and the second part is 80%.

Exam Tip: A quick mental check that the percentages add up to 100% can prevent simple calculation errors.

Question 2. (d) 1:2:5
Answer: The given ratio \( = 1 : 2 : 5 \). The sum of the terms of the ratio \( = 1 + 2 + 5 = 8 \). The first term as a percentage \( = \left( \frac{1}{8} \times 100 \right)\% = \frac{25}{2}\% = 12.5\% \). The second term as a percentage \( = \left( \frac{2}{8} \times 100 \right)\% = 25\% \). The third term as a percentage \( = \left( \frac{5}{8} \times 100 \right)\% = \frac{125}{2}\% = 62.5\% \).
In simple words: For the ratio 1:2:5, the total is 8 parts. The parts are 12.5%, 25%, and 62.5% when converted to percentages.

Exam Tip: Be careful with fractions when converting to decimals or percentages, especially when the denominator is not a factor of 100.

Question 3. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Answer: The original population \( = 25,000 \). The decreased population \( = 24,500 \). Therefore, the decrease in population \( = 25,000 - 24,500 = 500 \). The percentage decrease in population \( = \left[ \frac{\text{Decrease in population}}{\text{Original population}} \times 100 \right]\% \).
\( = \left[ \frac{500}{25000} \times 100 \right]\% \)
\( = 2\% \). The rate of decrease in population is 2%.
In simple words: The city's population dropped from 25,000 to 24,500, a decrease of 500 people. This represents a 2% decline in population.

Exam Tip: Always use the original or initial value in the denominator when calculating percentage increase or decrease.

Question 4. Arun bought a car for Rs 3,50,000 and the next year its price increased to Rs 3,70,000. Find the percentage increase in the price of the car.
Answer: The original price of the car \( = \text{Rs } 3,50,000 \). The new price of the car \( = \text{Rs } 3,70,000 \). The increase in the price of the car \( = 3,70,000 - 3,50,000 = \text{Rs } 20,000 \). The percentage increase in the price of the car \( = \left[ \frac{\text{Increase in price}}{\text{Original price}} \times 100 \right]\% \).
\( = \left[ \frac{20000}{350000} \times 100 \right]\% \)
\( = \frac{40}{7}\% = 5\frac{5}{7}\% \). The percentage increase in the car's price is \( 5\frac{5}{7}\% \).
In simple words: Arun's car went from Rs 3,50,000 to Rs 3,70,000, which is an increase of Rs 20,000. This increase is a \( 5\frac{5}{7}\% \) rise in price.

Exam Tip: When dealing with large numbers, simplify fractions before multiplying by 100 to make calculations easier and reduce error potential.

Question 5. I bought a TV for Rs 10,000 and sold it for a 20% profit. How much money did I get from selling the TV?
Answer: The cost price of the TV \( = \text{Rs } 10,000 \). The profit on the sale of the TV \( = 20\% \). Therefore, the profit received from the sale of the TV \( = \) Cost Price \( \times \) Profit Percentage.
\( = 10,000 \times \frac{20}{100} \)
\( = \text{Rs } 2000 \). Now, the selling price of the TV \( = \) Cost Price \( + \) Profit \( = 10,000 + 2000 = \text{Rs } 12,000 \). I would have received Rs 12,000 from selling the TV.
In simple words: The TV cost Rs 10,000, and I made a 20% profit, which is Rs 2000. So, I sold the TV for Rs 12,000.

Exam Tip: Remember that selling price when there's a profit is Cost Price + Profit, and when there's a loss, it's Cost Price - Loss.

Question 6. Juhi sold a washing machine for Rs 13,500. She incurred a 20% loss. For how much did Juhi buy the washing machine?
Answer: Let the cost price of the washing machine \( = x \). Here, Cost Price \( - \) Loss \( = \) Selling Price.
\( \implies x - \text{Loss} = \text{Selling Price} \)
\( \implies x - (20\% \text{ of Cost Price}) = 13500 \)
\( \implies x - \left( x \times \frac{20}{100} \right) = 13500 \)
\( \implies x - \frac{x}{5} = 13500 \)
\( \implies \frac{5x-x}{5} = 13500 \)
\( \implies 4x = 13500 \times 5 \)
\( \implies x = \frac{13500 \times 5}{4} \)
\( \implies x = 3375 \times 5 \)
\( \implies x = 16875 \). Juhi must have bought the washing machine for Rs 16,875.
In simple words: Juhi sold a washing machine for Rs 13,500 and lost 20%. To find the original price, we calculated that she bought it for Rs 16,875.

Exam Tip: When working with loss percentages, it's often helpful to set up an equation where the cost price is the unknown variable.

Question 7. (i) In chalk, the ratio of calcium, carbon, and oxygen is 10:3:12. Find the percentage of carbon in chalk.
Answer: In chalk, the mixed ratio of calcium, carbon, and oxygen is \( 10 : 3 : 12 \). The sum of the terms of the ratio \( = 10 + 3 + 12 = 25 \). The percentage of carbon in chalk \( = \left( \frac{3}{25} \times 100 \right)\% = 12\% \). Thus, the percentage of carbon in chalk is 12%.
In simple words: Chalk has calcium, carbon, and oxygen in a 10:3:12 ratio. The total parts are 25, meaning carbon makes up 12% of the chalk.

Exam Tip: Ensure you correctly identify which element's percentage is asked and use its corresponding ratio term in the calculation.

Question 7. (ii) If the weight of carbon in chalk is 3 grams, then find the total weight of the chalk.
Answer: Let the total weight of a piece of chalk be \( x \) grams. Chalk contains 12% carbon (from part (i)). The weight of carbon in it is 3 grams.
\( \implies x \times 12\% = 3 \)
\( \implies x \times \frac{12}{100} = 3 \)
\( \implies x = \frac{3 \times 100}{12} \)
\( \implies x = 25 \). Thus, the weight of the chalk is 25 grams.
In simple words: If 3 grams of carbon make up 12% of the chalk's weight, then the full chalk weighs 25 grams in total.

Exam Tip: When a percentage of a quantity is given, set up an equation to find the total quantity, where the percentage is expressed as a fraction or decimal.

Question 8. Amina buys a book for Rs 275 and sells it at a 15% loss. How much money did she sell the book for?
Answer: The cost price of the book \( = \text{Rs } 275 \). The percentage loss incurred on selling the book \( = 15\% \). Therefore, the loss incurred on selling the book \( = \) Cost Price \( \times \) Loss Percentage.
\( = \left( 275 \times \frac{15}{100} \right) = \text{Rs } 41.25 \). Now, the selling price of the book \( = \) Cost Price \( - \) Loss \( = 275 - 41.25 = \text{Rs } 233.75 \). Amina would have sold the book for Rs 233.75.
In simple words: Amina bought a book for Rs 275 and lost 15%, which is Rs 41.25. So, she sold the book for Rs 233.75.

Exam Tip: Always subtract the loss amount from the cost price to find the selling price when a loss occurs.

Question 9. Find the amount for the following sum for 3 years:
(a) Principal \( = \) Rs 1200, Annual interest rate \( = 12\% \)
Answer: Here, Principal \( P = \text{Rs } 1200 \), Interest Rate \( R = 12\% \), and Time \( T = 3 \) years. The simple interest \( = \frac{P \times R \times T}{100} \).
\( = \frac{1200 \times 12 \times 3}{100} \)
\( = 432 \). The amount \( = \) Principal \( + \) Interest \( = 1200 + 432 = 1632 \).
In simple words: With a principal of Rs 1200 at 12% interest for 3 years, the simple interest is Rs 432. The total amount to be paid back is Rs 1632.

Exam Tip: Clearly list the given values for principal, rate, and time before applying the simple interest formula to prevent mistakes.

Question 9. (b) Principal \( = \) Rs 7500, Annual interest rate \( = 5\% \)
Answer: Here, Principal \( P = \text{Rs } 7500 \), Interest Rate \( R = 5\% \), and Time \( T = 3 \) years. The simple interest \( = \frac{P \times R \times T}{100} \).
\( = \frac{7500 \times 5 \times 3}{100} \)
\( = \text{Rs } 1125 \). The amount \( = \) Principal \( + \) Interest \( = 7500 + 1125 = \text{Rs } 8625 \).
In simple words: For a principal of Rs 7500 at 5% interest for 3 years, the simple interest comes to Rs 1125, making the total amount Rs 8625.

Exam Tip: Double-check the multiplication and division in the simple interest formula, especially when dealing with multiple digits.

Question 10. At what percentage interest rate will Rs 56,000 yield an interest of Rs 280 in 2 years?
Answer: Here, Principal \( P = \text{Rs } 56,000 \), Interest Rate \( R = ? \), Time \( T = 2 \) years, Interest \( = \text{Rs } 280 \). The simple interest \( = \frac{P \times R \times T}{100} \).
\( \implies 280 = \frac{56000 \times R \times 2}{100} \)
\( \implies 280 = 560 \times R \times 2 \)
\( \implies R = \frac{280}{2 \times 560} \)
\( \implies R = \frac{1}{4}\% \)
\( \implies R = 0.25\% \). The interest rate is 0.25%.
In simple words: To get Rs 280 interest on Rs 56,000 in 2 years, the annual interest rate needed is 0.25%.

Exam Tip: When the rate is unknown, rearrange the simple interest formula to solve for R, \( R = \frac{\text{Simple Interest} \times 100}{P \times T} \).

Question 11. If Meena pays an interest of Rs 45 for one year at a 9% annual rate on a certain amount borrowed, find the amount she borrowed.
Answer: Here, Principal \( P = ? \), Interest Rate \( R = 9\% \), Time \( T = 1 \) year, Simple Interest \( = \text{Rs } 45 \). The simple interest \( = \frac{P \times R \times T}{100} \).
\( \implies 45 = \frac{P \times 9 \times 1}{100} \)
\( \implies P = \frac{45 \times 100}{9 \times 1} \)
\( \implies P = 500 \). The amount borrowed is Rs 500.
In simple words: Meena paid Rs 45 interest at a 9% rate for one year. This means she must have borrowed Rs 500 originally.

Exam Tip: When the principal is unknown, rearrange the simple interest formula to solve for P, \( P = \frac{\text{Simple Interest} \times 100}{R \times T} \).