Comparing Quantities — Class 7 IMO

Percentage

Percent means per hundred (out of 100). Percent problems appear in everyday life as discounts, taxes, and markups.

Problem Type	Formula
Discount	Discount = Original Price x Discount%. Sale Price = Original - Discount
Tax	Tax = Price x Tax%. Total = Price + Tax
Markup	Markup = Cost x Markup%. Selling Price = Cost + Markup
Percent Increase	(New - Old) / Old x 100%
Percent Decrease	(Old - New) / Old x 100%

Always convert percent to decimal first: 25% = 0.25

PERCENT CHANGE NUMBER LINE:

0%              100%            150%            200%
|----------------|----------------|----------------|
Original        Double           1.5x            2x

CONVERT % TO DECIMAL:
  25% = 25/100 = 0.25
  8%  = 8/100  = 0.08
  50% = 50/100 = 0.50

Example 1: Find 20% of 150.

(20/100) × 150 = 30.

Example 2: 25% of a number is 50. Find the number.

50 × (100/25) = 200.

Example 3: A $80 shirt is 25% off. What is the sale price?

Discount = 80 x 0.25 = $20. Sale price = 80 - 20 = $60.

Example 4: A $50 meal has 8% tax. What is the total bill?

Tax = 50 x 0.08 = $4. Total = 50 + 4 = $54.

Example 5: A town's population grew from 2,000 to 2,500. What is the percent increase?

(2500 - 2000) / 2000 x 100 = 500/2000 x 100 = 25%

Quick recap

Percentage of a number: multiply by the percentage as a fraction.
Find the whole: divide the part by the percentage and multiply by 100.
Convert % to decimal: divide by 100 (25% = 0.25)
Discount = subtract; Tax/Markup = add
Percent increase/decrease = (change / original) x 100
Original price = Sale price / (1 - discount rate)

✓ Quick check

What is 10% of 250?

(10/100) × 250 = 25.

Write ½ as a percentage.

½ × 100 = 50%.

Profit, Loss, CP & SP

The cost price (CP) is what an item costs and the selling price (SP) is what it sells for. Profit = SP − CP and Loss = CP − SP. The percentages are found on the CP: profit% = (profit ÷ CP) × 100.

Example 1: CP = ₹200, SP = ₹250. Find the profit%.

Profit = ₹50; profit% = (50 ÷ 200) × 100 = 25%.

Example 2: CP = ₹400, SP = ₹360. Find the loss%.

Loss = ₹40; loss% = (40 ÷ 400) × 100 = 10%.

Quick recap

Profit = SP − CP; Loss = CP − SP.
Profit% and loss% are calculated on the CP.

✓ Quick check

CP = ₹100, SP = ₹130. What is the profit%?

Profit = ₹30; profit% = (30 ÷ 100) × 100 = 30%.

Profit = SP − ___ ?

Profit = SP − CP.

Simple Interest, Discount & GST

Simple interest is SI = (P × R × T) ÷ 100, and the amount is P + SI. A discount is a percentage off the marked price. GST is a tax added on, such as 18% GST adding ₹18 on every ₹100.

Example 1: Find the SI on ₹1000 at 5% for 2 years and the amount.

SI = (1000 × 5 × 2) ÷ 100 = ₹100; amount = ₹1100.

Example 2: A ₹500 item has a 10% discount. What do you pay?

10% of 500 = ₹50 off, so you pay ₹450.

Quick recap

SI = (P × R × T) ÷ 100; amount = P + SI.
Discount reduces the price; GST adds tax on.

✓ Quick check

Find the SI on ₹2000 at 10% for 1 year.

SI = (2000 × 10 × 1) ÷ 100 = ₹200.

What is 18% GST on ₹100?

18% of ₹100 = ₹18.