Comparing Quantities
Overview
Comparing Quantities is a chapter in Class 7 Maths that teaches students how to compare two or more quantities using ratios, percentages, and fractions. Students learn to convert ratios to percentages, find percentage increase or decrease, calculate simple interest, and solve real-life problems involving profit, loss, and interest. This chapter builds strong foundations for financial mathematics and everyday problem-solving skills.
Typed Notes
Ratios and Equivalent Ratios
A ratio is a way of comparing two quantities of the same unit. For example, if there are 3 boys and 5 girls, the ratio of boys to girls is 3:5. Equivalent ratios are formed by multiplying or dividing both terms by the same number, just like equivalent fractions. For example, 3:5 = 6:10 = 9:15. To compare ratios, we convert them to fractions and find a common denominator. Ratios help us understand proportions in maps, recipes, and many real-life situations.
Percentages — Meaning and Conversions
Percentage means 'out of hundred' and is written with the symbol %. To convert a fraction to a percentage, multiply by 100. For example, 3/4 = (3/4) × 100 = 75%. To convert a percentage to a fraction, divide by 100. For example, 40% = 40/100 = 2/5. To find a percentage of a quantity, multiply the quantity by the percentage divided by 100. For example, 20% of 150 = (20/100) × 150 = 30. Percentages are used in marks, discounts, taxes, and statistics.
Profit, Loss, and Discount
When a shopkeeper sells an article for more than its cost price, he makes a profit. When he sells for less, he makes a loss. Profit % and Loss % are always calculated on the Cost Price. Discount is a reduction given on the Marked Price of an article. Discount % = (Discount/Marked Price) × 100. Selling Price = Marked Price − Discount. For example, if a shirt has a marked price of ₹500 and a 10% discount, discount = ₹50, so selling price = ₹450. These concepts are used in everyday shopping.
Simple Interest
When money is borrowed or deposited in a bank, interest is charged or earned. Simple Interest (SI) is calculated only on the original principal for every year. The formula is SI = (P × R × T) / 100, where P is Principal, R is Rate of interest per annum, and T is Time in years. Amount = Principal + Simple Interest. For example, if P = ₹1000, R = 5%, T = 2 years, then SI = (1000 × 5 × 2)/100 = ₹100, and Amount = ₹1100. Simple interest is used in loans and savings.
Key Concepts
Revision ke liye ek nazar — exam se pehle yahi padhna hai.
- 01A ratio compares two quantities of the same kind; it can be written as a:b or a/b.
- 02Percentage means per hundred; to convert a fraction to percentage, multiply by 100.
- 03Profit = Selling Price − Cost Price; Loss = Cost Price − Selling Price.
- 04Profit % = (Profit/Cost Price) × 100; Loss % = (Loss/Cost Price) × 100.
- 05Simple Interest (SI) = (Principal × Rate × Time) / 100; Amount = Principal + SI.
Important Formulas
Questions & Solutions
Pehle khud try karo — phir solution kholo. Yahi tariqa topper banata hai.
A shopkeeper bought a bicycle for ₹1,200 and sold it for ₹1,500. Find the profit and profit percentage.
Find the simple interest on ₹5,000 at 8% per annum for 3 years. Also find the total amount.
A shirt is marked at ₹800. A discount of 15% is given. Find the discount amount and the selling price.
Convert 3/8 into a percentage and also express 65% as a fraction in its simplest form.
In a class of 40 students, 25 are girls. What percentage of students are boys?
Comparing Quantities covers ratios, percentages, profit and loss, discount, and simple interest. Ratios compare two quantities; percentages express values per hundred. Profit and loss percentages are calculated on cost price, while discount is calculated on marked price. Simple Interest is computed using SI = PRT/100, and Amount = Principal + SI. These concepts are essential for solving real-life financial problems confidently.
Chapter-end quiz
4 MCQsOption tap karo — turant pata chalega sahi ya galat, explanation ke saath.
Q1.What is 30% of 250?
Q2.A toy is bought for ₹400 and sold for ₹360. What is the loss percentage?
Q3.Simple Interest on ₹2000 at 5% per annum for 2 years is:
Q4.A jacket is marked at ₹1000 with a 20% discount. What is the selling price?
Mark karo — dashboard par progress dikhega.