Earning: gross pay and ways to be paid
Gross pay = everything you earn before deductions.
- Hourly wage: hours × rate. 38 h × 250 = 9,500.
- Overtime: extra hours, often paid at 1.5 × rate ("time and a half").
- Salary: a fixed amount per year or month, whatever the hours.
- Commission: a percentage of sales (5% of 80,000 = 4,000).
- Piecework: paid per item made. Tips and bonus add to earnings.
Pay schedules: weekly (52 pays a year), every two weeks (26), twice a month (24), monthly (12). Salary ÷ number of pays = each payment. Steady salary helps budgeting; commission can pay more but changes month to month.
Deductions, net pay and purchasing power
Deductions are taken off before you are paid: income tax, pension / provident fund (retirement saving), social or health insurance, and sometimes union fees.
Net pay = gross pay − total deductions. Example: 10,000 − (1,000 + 1,200 + 300) = 7,500.
Purchasing power is how much your money can buy. If prices rise (inflation) and pay does not, purchasing power falls. Compare jobs or cities by what net pay buys after rent, food and travel, not by gross pay alone.
Purchasing: discounts, sales tax, unit price and change
Discount: sale price = price × (1 − d). 25% off 800 → 800 × 0.75 = 600. Estimate first: 10% of 800 is 80, so 25% is about 200.
Sales tax (GST, VAT): total = sale price × (1 + t). 600 × 1.10 = 660. Some prices already include tax; read the label.
Unit price = price ÷ quantity. 500 g for 60 → 12 per 100 g; 1 kg for 110 → 11 per 100 g.
Change: count up from the bill to the money given (660 → 700 → 1000: change 340).
Extra costs: card or online fees, delivery, interest on instalments, extended warranties. A good decision compares total cost, need, quality and budget.
Owning a vehicle and comparing ways to travel
Licence: learner then full licence; new drivers often have limits (no night driving, zero alcohol). Unsafe driving (speeding, phone use, drink-driving) brings fines, points and higher insurance.
Buying: new (costly, warranty) or used (cheaper, check history and condition); buy, lease or rent. Add registration, taxes and loan interest.
Insurance costs more for young or new drivers, costly cars and drivers with past claims.
Fuel cost = distance × (litres per 100 km) ÷ 100 × price per litre. 300 km at 6 L/100 km and 100 per litre → 18 L → 1,800.
Map distance: map length × scale. 4 cm on a 1 : 2,500,000 map = 100 km. Choose a route by distance, time, tolls and safety.
Compare car, bus, train and plane by total cost, time, comfort and emissions. Renting a van or trailer can be cheaper than owning one for a one-time move.
Try it
Use the free-play sliders: set a trip you know (e.g. home to a relative's town). Note the car cost. Then look up a bus or train ticket for each person in your family. Which is cheaper? Which is faster?
Key formulas and definitions
- Gross pay = hours × rate (+ overtime hours × 1.5 × rate)
- Net pay = gross pay − deductions
- Sale price = price × (1 − discount rate); Total = sale price × (1 + tax rate)
- Unit price = price ÷ quantity
- Fuel cost = distance × (L per 100 km) ÷ 100 × price per L
- Real distance = map distance × scale
Worked examples
1. Riya works 40 h at 200 per hour and 5 h overtime at time and a half. Find gross pay.
Normal: 40 × 200 = 8,000. Overtime rate: 1.5 × 200 = 300. Overtime: 5 × 300 = 1,500. Gross = 9,500.
2. A salary is 4,80,000 per year paid monthly. Find each payment.
4,80,000 ÷ 12 = 40,000 per month.
3. Gross pay 30,000. Tax 10%, pension 12%, insurance 500. Find net pay.
Tax: 3,000. Pension: 3,600. Total deductions: 3,000 + 3,600 + 500 = 7,100. Net = 30,000 − 7,100 = 22,900.
4. A jacket costs 2,400 with 30% off and 12% GST. Find the total.
Sale price: 2,400 × 0.70 = 1,680. Total: 1,680 × 1.12 = 1,881.60.
5. Rice: 2 kg for 150 or 5 kg for 360. Which is the better buy?
2 kg: 150 ÷ 2 = 75 per kg. 5 kg: 360 ÷ 5 = 72 per kg. The 5 kg bag is cheaper per kg (if you will use it).
6. A 450 km trip, car uses 7 L/100 km, fuel 105 per litre, tolls 400. Four people. Train ticket 500 each. Which is cheaper?
Fuel: 450 × 7 ÷ 100 = 31.5 L; 31.5 × 105 = 3,307.50. Car total: 3,307.50 + 400 = 3,707.50. Train: 4 × 500 = 2,000. The train is cheaper by 1,707.50 (one way).
Common mistakes
- Thinking net pay equals gross pay. Deductions always come off first.
- Adding the discount percent and tax percent together (25% off, 10% tax ≠ 15% off). Multiply step by step.
- Comparing pack prices instead of unit prices. Divide by the quantity first.
- Counting only fuel as the cost of a car. Insurance, repairs, loan, licence and parking add a lot.