Money
Profit & Loss with Percentage
Profit = SP − CP and Loss = CP − SP, where CP is the cost price and SP the selling price. To find profit percent, use (profit ÷ CP) × 100; for loss percent, use (loss ÷ CP) × 100.
If CP = ₹100 and SP = ₹120, profit = ₹20 and profit% = (20 ÷ 100) × 100 = 20%.
Example 1: CP = ₹100, SP = ₹120. Find the profit and profit%.
Profit = ₹20; profit% = (20 ÷ 100) × 100 = 20%.
Example 2: CP = ₹200, SP = ₹150. Find the loss and loss%.
Loss = ₹50; loss% = (50 ÷ 200) × 100 = 25%.
Quick recap
- Profit = SP − CP; Loss = CP − SP.
- Profit% = (profit ÷ CP) × 100; Loss% = (loss ÷ CP) × 100.
✓ Quick check
CP = ₹50, SP = ₹60. What is the profit percent?
Profit = ₹10; profit% = (10 ÷ 50) × 100 = 20%.
CP = ₹100, SP = ₹80. What is the loss percent?
Loss = ₹20; loss% = (20 ÷ 100) × 100 = 20%.
Simple Interest
When money (the principal P) is kept in a bank, it earns simple interest. The formula is SI = (P × R × T) ÷ 100, where R is the rate per year (%) and T is the time in years.
For P = ₹1000, R = 5% and T = 2 years: SI = (1000 × 5 × 2) ÷ 100 = ₹100.
Example 1: Find the simple interest on ₹1000 at 5% for 2 years.
SI = (1000 × 5 × 2) ÷ 100 = ₹100.
Example 2: Find the simple interest on ₹2000 at 10% for 1 year.
SI = (2000 × 10 × 1) ÷ 100 = ₹200.
Quick recap
- SI = (P × R × T) ÷ 100.
- P = principal, R = rate per year, T = time in years.
✓ Quick check
Find the SI on ₹500 at 10% for 2 years.
SI = (500 × 10 × 2) ÷ 100 = ₹100.
Find the SI on ₹1000 at 4% for 3 years.
SI = (1000 × 4 × 3) ÷ 100 = ₹120.
Unitary Method, Bills & Discounts
The unitary method finds the value of one item, then scales up. If 5 pens cost ₹100, one pen costs ₹20, so 8 pens cost ₹160.
A discount is a percentage off the price. A 10% discount on ₹500 means ₹50 off, so you pay ₹450.
Example 1: 5 pens cost ₹100. What do 8 pens cost?
One pen = ₹20, so 8 pens = ₹160.
Example 2: A ₹500 item has a 10% discount. What do you pay?
10% of 500 = ₹50 off, so you pay ₹450.
Quick recap
- Unitary method: find the value of one, then multiply.
- Price after discount = price − discount amount.
✓ Quick check
3 kg of rice cost ₹150. What do 5 kg cost?
1 kg = ₹50, so 5 kg = ₹250.
A ₹400 item has a 20% discount. How much is taken off?
20% of 400 = ₹80.
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