Explore the key concepts of “Exercise 7.2 Comparing Quantities” through these essential formulas and examples. Understanding these concepts will help you to compare different quantities in various cases.
Essential concepts for solving Comparing Quantities Exercise 7.2
Understanding Cost and Selling Prices
Cost Price (CP): The price at which an item is purchased.
Selling Price (SP): The price at which an item is sold.
Profit: If CP < SP, Profit = SP – CP.
Loss: If CP > SP, Loss = CP – SP.
Example: Buy a book for ₹100 (CP) and sell it for ₹120 (SP), Profit = ₹120 – ₹100 = ₹20.
Simple Interest on Loans
Principal: The original amount borrowed.
Interest: The extra amount paid for borrowing.
Simple Interest Formula: I = (PRT)/100, where P is Principal, R is Rate, and T is Time.
Total Amount to Repay: A = P + I.
Example: Borrow ₹1000 at 10% p.a. for 1 year, Interest = (1000 x 10 x 1)/100 = ₹100.
Calculating Ratios in Percentages
Ratio: A comparison of two quantities.
Percentage of Ratio Component: (Part of Ratio / Total of All Parts) x 100%.
Example: In a ratio 1:3, for the first part: (1/(1+3)) x 100% = 25%.
Percentages in Daily Life
Percentage: A way of expressing a number as a fraction of 100.
Discount Calculation: Discount = (Discount Percent x Original Price) / 100.
Interest Calculation: Interest = (Principal x Rate x Time) / 100.
Example: 20% discount on ₹500 item, Discount = (20 x 500)/100 = ₹100.
NCERT Solutions for Class 7 Maths Exercise 7.1 Chapter 7 Comparing Quantities
1. Tell what is the profit or loss in the following transactions. Also find profit per cent or loss per cent in each case.
(a) Gardening shears bought for ₹ 250 and sold for ₹ 325.
Profit = Selling Price – Cost Price
= ₹ 325 – ₹ 250 = ₹ 75
Profit Percent = (Profit / Cost Price) x 100
= (₹ 75 / ₹ 250) x 100 = 30%
(b) A refrigerator bought for ₹ 12,000 and sold at ₹ 13,500.
Cost Price = ₹ 12,000
Selling Price = ₹ 13,500
S.P. > C.P.
Therefore, profit is made
Profit = S.P. – C.P.
Profit = ₹ 13,500 – ₹ 12,000 = ₹ 1,500
Profit Percentage = (Profit/C.P.) x 100%
Profit Percent = (₹ 1,500 / ₹ 12,000) x 100 = 12.5%
(c) A cupboard bought for ₹ 2,500 and sold at ₹ 3,000.
Cost Price = ₹ 2,500
Selling Price = ₹ 3,000
S.P. > C.P.
Therefore, profit is made
Profit = S.P. – C.P.
Profit = ₹ 3,000 – ₹ 2,500 = ₹ 500
Profit Percentage = (Profit/C.P.) x 100%
Profit Percent = (₹ 500 / ₹ 2,500) x 100 = 20%
(d) A skirt bought for ₹ 250 and sold at ₹ 150.
Cost Price = ₹ 250
Selling Price = ₹ 150
C.P. > S.P.
Therefore, Loss is made
Loss = Cost Price – Selling Price
= ₹ 250 – ₹ 150 = ₹ 100
Loss Percent = (Loss / Cost Price) x 100
= (₹ 100 / ₹ 250) x 100 = 40%
2. Convert each part of the ratio to percentage:
(a) 3 : 1
Total parts = 3 + 1 = 4
3 out of 4 = (3/4) x 100% = 75%
1 out of 4 = (1/4) x 100% = 25%
(b) 2 : 3 : 5
Total parts = 2 + 3 + 5 = 10
2 out of 10 = (2/10) x 100% = 20%
3 out of 10 = (3/10) x 100% = 30%
5 out of 10 = (5/10) x 100% = 50%
(c) 1:4
Total parts = 1 + 4 = 5
1 out of 5 = (1/5) x 100% = 20%
4 out of 5 = (4/5) x 100% = 80%
(d) 1 : 2 : 5
Total parts = 1 + 2 + 5 = 8
1 out of 8 = (1/8) x 100% = 12.5%
2 out of 8 = (2/8) x 100% = 25%
5 out of 8 = (5/8) x 100% = 62.5%
3. The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.
Initial population = 25,000
Decreased population = 24,500
Decrease = 25,000 – 24,500 = 500
Percentage Decrease = (Decrease / Initial population) x 100
= (500 / 25,000) x 100 = 2%
4. Arun bought a car for ₹ 3,50,000. The next year, the price went upto ₹ 3,70,000. What was the Percentage of price increase?
Initial price of the car = ₹ 3,50,000
New price of the car = ₹ 3,70,000
Price increase = ₹ 3,70,000 – ₹ 3,50,000 = ₹ 20,000
Percentage Increase = (Price Increase / Initial Price) x 100
= (₹ 20,000 / ₹ 3,50,000) x 100 = 5.71%
5. I buy a T.V. for ₹ 10,000 and sell it at a profit of 20%. How much money do I get for it?
Selling price of a T.V. bought at ₹ 10,000 and sold at a profit of 20%.
Profit Percent = 20%
Profit = (Profit Percent / 100) x Cost Price
= (20 / 100) x ₹ 10,000 = ₹ 2,000
Selling Price = Cost Price + Profit
= ₹ 10,000 + ₹ 2,000 = ₹ 12,000
6. Juhi sells a washing machine for ₹ 13,500. She loses 20% in the bargain. What was the price at which she bought it?
Cost price of a washing machine sold at ₹ 13,500 with a loss of 20%.
Loss Percent = 20%
Selling Price = ₹ 13,500
Loss = (Loss Percent / 100) x Cost Price
Cost Price = Selling Price / (1 – Loss Percent / 100)
Cost Price = ₹ 13,500 / (1 – 20 / 100)
Cost Price = ₹ 13,500 / 0.8
Cost Price = ₹ 16,875
7. (i) Chalk contains calcium, carbon and oxygen in the ratio 10:3:12. Find the percentage of carbon in chalk.
Percentage of carbon in chalk with a ratio of calcium, carbon, and oxygen as 10:3:12.
Total parts in the ratio = 10 + 3 + 12 = 25
Carbon’s part = 3
Percentage of Carbon = (Carbon’s part / Total parts) x 100
Percentage of Carbon = (3 / 25) x 100
Percentage of Carbon = 12%
(ii) If in a stick of chalk, carbon is 3g, what is the weight of the chalk stick?
Weight of the chalk stick if carbon is 3g.
Total parts in the ratio = 25
Carbon’s part = 3g corresponds to 3 parts of the ratio.
Weight of the chalk stick = (Total weight / Carbon’s parts) x Total parts in the ratio
Weight of the chalk stick = (3g / 3) x 25
Weight of the chalk stick = 1g x 25
Weight of the chalk stick = 25g
8. Amina buys a book for ₹ 275 and sells it at a loss of 15%. How much does she sell it for?
Selling price of a book bought for ₹ 275 and sold at a loss of 15%.
Loss Percent = 15%
Cost Price = ₹ 275
Loss = (Loss Percent / 100) x Cost Price
Loss = (15 / 100) x ₹ 275
Loss = ₹ 41.25
Selling Price = Cost Price – Loss
Selling Price = ₹ 275 – ₹ 41.25
Selling Price = ₹ 233.75
9. Find the amount to be paid at the end of 3 years in each case:
Amount to be paid at the end of 3 years at a certain rate of interest.
(a) Principal = ₹ 1,200 at 12% p.a. for 3 years.
Simple Interest = (Principal x Rate x Time) / 100
Simple Interest = (₹ 1,200 x 12 x 3) / 100
Simple Interest = ₹ 432
Amount = Principal + Simple Interest
Amount = ₹ 1,200 + ₹ 432
Amount = ₹ 1,632
(b) Principal = ₹ 7,500 at 5% p.a. for 3 years.
Simple Interest = (Principal x Rate x Time) / 100
Simple Interest = (₹ 7,500 x 5 x 3) / 100
Simple Interest = ₹ 1,125
Amount = Principal + Simple Interest
Amount = ₹ 7,500 + ₹ 1,125
Amount = ₹ 8,625
10. What rate gives ₹ 280 as interest on a sum of ₹ 56,000 in 2 years?
Rate of interest for ₹ 280 interest on a principal of ₹ 56,000 in 2 years.
Interest = ₹ 280
Principal = ₹ 56,000
Time = 2 years
Rate = (Interest x 100) / (Principal x Time)
Rate = (₹ 280 x 100) / (₹ 56,000 x 2)
Rate = 0.25%
11. If Meena gives an interest of ₹ 45 for one year at 9% rate p.a.. What is the sum she has borrowed?
Sum borrowed if Meena pays ₹ 45 as interest for one year at 9% rate p.a..
Interest = ₹ 45
Rate = 9%
Time = 1 year
Principal = (Interest x 100) / (Rate x Time)
Principal = (₹ 45 x 100) / (9 x 1)
Principal = ₹ 500
Additional Worksheet Questions for Exercise 7.2 Comparing Quantities
- If the price of a laptop increases by 15% to ₹46,000, what was the original price?
- A jar contains a 40% sugar solution. If 15 liters of water is added to 10 liters of this solution, what is the percentage concentration of sugar in the new solution?
- A dress is listed at ₹2,000 and a discount of 25% is offered on the list price. What additional discount percent must be offered to bring the final price to ₹1,350?
- The population of a town is 55,000. It increases by 10% in the first year and then decreases by 10% in the second year. What is the population at the end of the second year?
- A plot of land is valued at ₹100,000. Its value appreciates by 10% in the first year and then depreciates by 10% in the second year. What is the value of the land at the end of two years?
- If 70% of a number is added to 112, the result is the number itself. Find the number.
- A shopkeeper claims to sell his goods at cost price but uses a weight of 800 grams for a kilogram. Find his actual profit percentage.
- In an election between two candidates, one gets 55% of the total valid votes. If the total votes were 20,000 and 20% of votes were invalid, what is the number of valid votes the other candidate got?
- A student scores 75% marks in one subject and 45% marks in a second subject, getting 60 marks more in the first subject than the second. What are the maximum marks for each subject?
- If the length of a rectangle is increased by 20% and the width is decreased by 20%, what is the effect on the area of the rectangle?
Worksheet Question Answers
- Original price = ₹46,000 / 1.15 = ₹40,000
- New concentration = (40% of 10 liters) / (10 liters + 15 liters) = 16%
- Additional discount = [(₹2,000 – ₹1,350) / ₹2,000] x 100 = 32.5%
- Population end of second year = 55,000 x 1.10 x 0.90 = 54,450
- Value end of two years = ₹100,000 x 1.10 x 0.90 = ₹99,000
- The number = 112 / (1 – 0.70) = 373.33
- Profit percentage = [(1,000 – 800) / 800] x 100 = 25%
- Valid votes for other candidate = 45% of 16,000 = 7,200
- Let maximum marks be x; 0.75x – 0.45x = 60; x = 400 for each subject
- Area change = (1.20 x 0.80) x original area = 0.96 x original area, a decrease of 4%
