Comparing Quantities Class 8th Math Notes

Comparing Quantities: We compare things all the time — such as prices, marks, and distances. Comparing quantities helps us find how much one value is more or less than another.

For example, if one pen costs ₹10 and another costs ₹20, the second one is twice as costly.

Mathematically, we use tools like ratio, percentage, and proportion to compare quantities in a proper way.

What is a Ratio?

A ratio is a way of comparing two quantities of the same kind and unit.
Example: If the cost of 2 pencils is ₹10, then the ratio of pencils to rupees is 2 : 10 or 1 : 5.
This means one pencil costs ₹5.

We simplify a ratio by dividing both parts with their highest common factor (HCF).
Example: 8 : 12 = (8 ÷ 4) : (12 ÷ 4) = 2 : 3.

Ratios are used in comparing prices, marks, ingredients, or distances.

What is Profit and Loss?

When something is sold, we may earn money (profit) or lose money (loss).

• Cost Price (C.P.) – Price at which an item is bought.
• Selling Price (S.P.) – Price at which an item is sold.

Formulas:

• Profit = S.P. – C.P.
• Loss = C.P. – S.P.
• Profit% = (Profit / C.P.) × 100
• Loss% = (Loss / C.P.) × 100

Example:
If a toy is bought for ₹100 and sold for ₹120,
Profit = 120 – 100 = ₹20
Profit% = (20 / 100) × 100 = 20%.

These ideas are useful in trade and daily purchases.

Discount

A discount is a reduction in the price of an item. Shops give discounts to attract buyers.

• Marked Price (M.P.) – Price before discount.
• Selling Price (S.P.) – Price after discount.

Formulas:

• Discount = M.P. – S.P.
• Discount% = (Discount / M.P.) × 100

Example:
If a bag’s marked price is ₹500 and discount is 10%,
Discount = (10/100) × 500 = ₹50
Selling Price = 500 – 50 = ₹450.

So, the buyer pays ₹450 after discount.

Compound Interest (C.I.)

Compound Interest is interest calculated on both the original amount and the interest added earlier.

Formula:
C.I. = Amount – Principal
Amount (A) = P (1 + R/100)ⁿ

Where,
P = Principal, R = Rate, n = Time (years)

Example:
If ₹1,000 is invested at 10% for 2 years,
A = 1000 (1 + 10/100)² = 1000 × (1.1)² = ₹1210
C.I. = 1210 – 1000 = ₹210.

Compound Interest is used in banks, savings, and loans.

Applications of Compound Interest

Compound Interest (C.I.) is widely used in our daily life. It helps us understand how money grows over time. Here are some common applications:

• Bank Savings: Used in savings accounts and fixed deposits to calculate interest on the principal amount over a period of time.
• Loans and EMIs: Used in home loans, car loans, and personal loans where interest is calculated on the total outstanding amount.
• Credit Cards: Calculated on outstanding balance in case of non-payment at the end of the billing cycle.
• Investments: Useful in calculating future value of investments such as mutual funds, bonds, etc.
• Business Growth: Used by businesses to calculate interest or profit on investments/capital.
• Financial Planning: Helpful in planning long-term financial goals such as education, property, retirement, etc.