What is the difference between ratio and proportion?

A ratio compares two quantities (e.g., $3 : 5$). A proportion states that two ratios are equal (e.g., $3 : 5 = 6 : 10$). Ratios are like fractions; proportions are like equations between fractions. You use proportions to find an unknown when you know three of the four values.

Why is profit/loss percentage always calculated on Cost Price?

By convention, profit and loss percentages are calculated on the Cost Price because that's the amount the seller invested. It tells the seller what percentage return they got on their investment. Calculating on SP would give a different (and misleading) result. This convention is standard across CBSE, ICSE, and all competitive exams.

Can a percentage be more than 100%?

Yes! A percentage greater than $100\%$ simply means the part is bigger than the whole being compared to. For example, if a population grew from $1{,}000$ to $2{,}500$, the new population is $250\%$ of the original. The increase is $150\%$. Similarly, if you score bonus marks that take your total above the maximum, your percentage can exceed $100$.

What is the difference between simple interest and compound interest?

In simple interest, the interest is calculated only on the original principal amount for every period. In compound interest (which you'll study in Class 8), the interest is calculated on the principal PLUS any accumulated interest. So compound interest grows faster. For example, Rs. $1{,}000$ at $10\%$ for $2$ years gives SI $=$ Rs. $200$ but CI $=$ Rs. $210$.

How do I find the original price when a discount percentage is given?

If an item costs Rs. $x$ after a discount of $d\%$, then the original price $= \frac{x \times 100}{100 - d}$. For example, if a shirt costs Rs. $680$ after a $15\%$ discount, the original price $= \frac{680 \times 100}{85} = $ Rs. $800$.

What is the difference between ratio and proportion?

A ratio compares two quantities (e.g., $3 : 5$). A proportion states that two ratios are equal (e.g., $3 : 5 = 6 : 10$). Ratios are like fractions; proportions are like equations between fractions. You use proportions to find an unknown when you know three of the four values.

Why is profit/loss percentage always calculated on Cost Price?

By convention, profit and loss percentages are calculated on the Cost Price because that's the amount the seller invested. It tells the seller what percentage return they got on their investment. Calculating on SP would give a different (and misleading) result. This convention is standard across CBSE, ICSE, and all competitive exams.

Can a percentage be more than 100%?

Yes! A percentage greater than $100\%$ simply means the part is bigger than the whole being compared to. For example, if a population grew from $1{,}000$ to $2{,}500$, the new population is $250\%$ of the original. The increase is $150\%$. Similarly, if you score bonus marks that take your total above the maximum, your percentage can exceed $100$.

What is the difference between simple interest and compound interest?

In simple interest, the interest is calculated only on the original principal amount for every period. In compound interest (which you'll study in Class 8), the interest is calculated on the principal PLUS any accumulated interest. So compound interest grows faster. For example, Rs. $1{,}000$ at $10\%$ for $2$ years gives SI $=$ Rs. $200$ but CI $=$ Rs. $210$.

How do I find the original price when a discount percentage is given?

If an item costs Rs. $x$ after a discount of $d\%$, then the original price $= \frac{x \times 100}{100 - d}$. For example, if a shirt costs Rs. $680$ after a $15\%$ discount, the original price $= \frac{680 \times 100}{85} = $ Rs. $800$.

Study Guide

Comparing Quantities Class 7: Ratio, Percentage, Profit & Loss

From shopping discounts to exam scores, learn the math behind everyday comparisons!

CBSEClass 7

The SparkEd Authors (IITian & Googler)15 March 202610 min read

Why Comparing Quantities Matters in Real Life

$"This shirt is 30% off!" "India scored at a run rate of 8.5." "The recipe needs flour and sugar in the ratio 3:1." Every single day, you compare quantities using ratios, percentages, and proportions.$

$In NCERT Class 7 Math (Chapter 7: Comparing Quantities), you'll learn the math behind these comparisons. This chapter is incredibly practical because you'll use these concepts in shopping, cooking, sports, science, and eventually in business and finance. Let's make you a pro at it!$

Ratios: Comparing Two Quantities

$A ratio compares two quantities of the same kind. It tells you how much of one thing there is compared to another.$

$a$

$3$

$18$

18 : 12 = 3 : 2

$3$

$40$

$1.2$

40 : 120 = 1 : 3

$Equivalent Ratios: Just like equivalent fractions, you can multiply or divide both parts of a ratio by the same number.$

2 : 5 = 4 : 10 = 6 : 15 = 20 : 50

Percentages: The Universal Comparison Tool

$100$

\text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100

Converting Fractions to Percentages

$100$

\frac{3}{4} = \frac{3}{4} \times 100\% = 75\%

\frac{1}{8} = \frac{1}{8} \times 100\% = 12.5\%

\frac{5}{6} = \frac{5}{6} \times 100\% = 83.\overline{3}\%

Converting Decimals to Percentages

$100$

0.45 = 45\%

0.07 = 7\%

1.25 = 125\%

$100\%$

Converting Percentages to Fractions

$100$

25\% = \frac{25}{100} = \frac{1}{4}

37.5\% = \frac{37.5}{100} = \frac{375}{1000} = \frac{3}{8}

$Memorising common fraction-percentage equivalents speeds up calculations:$

$Fraction$	$Percentage$
$\frac{1}{2}$	$50\%$
$\frac{1}{4}$	$25\%$
$\frac{3}{4}$	$75\%$
$\frac{1}{5}$	$20\%$
$\frac{1}{3}$	$33.\overline{3}\%$
$\frac{1}{8}$	$12.5\%$

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Percentage Applications: Increase, Decrease & Finding the Whole

$Percentages are used in all sorts of practical calculations.$

$15\%$

\frac{15}{100} \times 600 = 90

$50{,}000$

\text{Increase} = 55{,}000 - 50{,}000 = 5{,}000

\text{Percentage increase} = \frac{5{,}000}{50{,}000} \times 100 = 10\%

$800$

\text{Decrease} = 800 - 680 = 120

\text{Percentage decrease} = \frac{120}{800} \times 100 = 15\%

$40\%$

\frac{40}{100} \times x = 120

x = \frac{120 \times 100}{40} = 300

Profit, Loss & Discount

$When a shopkeeper buys an item, that's the Cost Price (CP) . When they sell it, that's the Selling Price (SP) .$

$SP > CP$

$Percentage formulas:$

\text{Profit}\% = \frac{\text{Profit}}{CP} \times 100 = \frac{SP - CP}{CP} \times 100

\text{Loss}\% = \frac{\text{Loss}}{CP} \times 100 = \frac{CP - SP}{CP} \times 100

$250$

\text{Profit} = 300 - 250 = \text{Rs. } 50

\text{Profit}\% = \frac{50}{250} \times 100 = 20\%

$15{,}000$

\text{Loss} = 15{,}000 - 12{,}000 = \text{Rs. } 3{,}000

\text{Loss}\% = \frac{3{,}000}{15{,}000} \times 100 = 20\%

$Finding SP from CP and profit/loss percentage:$

SP = CP + \text{Profit} = CP \times \left(1 + \frac{\text{Profit}\%}{100}\right)

SP = CP - \text{Loss} = CP \times \left(1 - \frac{\text{Loss}\%}{100}\right)

$=$

SP = 400 \times \left(1 + \frac{15}{100}\right) = 400 \times 1.15 = \text{Rs. } 460

Simple Interest

$When you borrow or deposit money, interest is the extra amount paid for using that money.$

$Key terms: - Principal (P): The original amount borrowed or deposited. - Rate (R): The percentage charged per year. - Time (T): The duration in years. - Simple Interest (SI): Interest calculated only on the principal.$

SI = \frac{P \times R \times T}{100}

\text{Amount (A)} = P + SI = P + \frac{P \times R \times T}{100} = P\left(1 + \frac{RT}{100}\right)

$5{,}000$

SI = \frac{5000 \times 8 \times 3}{100} = \frac{120000}{100} = \text{Rs. } 1{,}200

\text{Amount} = 5000 + 1200 = \text{Rs. } 6{,}200

$2{,}000$

300 = \frac{2000 \times R \times 2}{100}

300 = 40R

R = 7.5\%

$1{,}600$

SI = 2000 - 1600 = 400

400 = \frac{1600 \times 5 \times T}{100}

400 = 80T

T = 5 \text{ years}

Common Mistakes to Watch Out For

$These errors come up again and again in exams:$

$1. Calculating profit/loss percentage on SP instead of CP : Profit and loss percentages are ALWAYS calculated on the Cost Price, not the Selling Price. This is the most common mistake!$

$500$

$25\%$

$6$

$12 : 8$

Key Takeaways

$Here's your essential summary:$

$a : b$

$Ready for some practice? Head to SparkEd and try the interactive questions on ratios, percentages, and profit & loss. The instant feedback helps you learn from every mistake!$

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