Switch2Learning

Mathematics · Chapter 1: Introduction to Mathematics

Mathematics in Daily Life and Careers

Mathematics in daily life with worked examples (discounts, electricity units, speed, run rate, Zakat), key formulas, and careers that need maths in Pakistan.

Taught in Class 9Class 10Class 11Class 12O LevelA Level

Key termRememberExampleWatch out

01Concept

You use mathematics every day, often without noticing. Here are some everyday calculations, worked out step by step.

Worked examples from daily life

1. A discount in a sale. A shirt costs Rs 2,400 and is on sale at 25% off.

  • Discount = 25% of 2,400 = 25 ÷ 100 × 2,400 = Rs 600
  • Sale price = 2,400 − 600 = Rs 1,800

2. Units on an electricity bill. An air conditioner of 1.5 kW runs for 8 hours.

  • Energy = power × time = 1.5 kW × 8 h = 12 kWh
  • One unit on the bill is 1 kWh, so the AC uses 12 units in one day.

3. Travel time. A bus travels 160 km at an average speed of 80 km/h.

  • Time = distance ÷ speed = 160 ÷ 80 = 2 hours

4. Run rate in cricket. A team scores 150 runs in 20 overs.

  • Run rate = runs ÷ overs = 150 ÷ 20 = 7.5 runs per over

5. Zakat. Zakat is 2.5% (one-fortieth) of eligible savings held for a full lunar year. On savings of Rs 200,000:

  • Zakat = 2.5 ÷ 100 × 200,000 = Rs 5,000

Careers that need mathematics

CareerHow they use maths
Engineer (civil, electrical, mechanical, software)Calculations for bridges, circuits, machines and programs
Chartered accountantAccounts, tax and audits (through ICAP in Pakistan)
Banker / financial analystInterest, loans and investments
ActuaryUses probability and statistics to price insurance
Statistician / data scientistAnalyses large amounts of data to find patterns
Software developerAlgorithms and logic
ArchitectGeometry, measurement and scale drawings
EconomistModels of prices, growth and trade
Mathematics teacher / lecturerTeaching at schools, colleges and universities

How to get there

  1. Class 9–10: Science group with mathematics.
  2. Class 11–12: Pre-Engineering or ICS (Computer Science); both include mathematics. For accounting and business, I.Com also works.
  3. University (4 years): BS Mathematics, BS Statistics, BS Computer Science, BE Engineering or BS Actuarial Science. For accounting, the CA qualification through ICAP.
  4. After the degree: MS/MPhil or PhD for research and university teaching.

02Key Formulas

Percentage of an amount

Part=Percentage100×Whole\text{Part} = \frac{\text{Percentage}}{100} \times \text{Whole}

25% of 2,400 = 600.

Average (mean)

Average=Sum of valuesNumber of values\text{Average} = \frac{\text{Sum of values}}{\text{Number of values}}

Marks 60, 70, 80: average = 210 ÷ 3 = 70.

Speed, distance and time

Speed=DistanceTime\text{Speed} = \frac{\text{Distance}}{\text{Time}}

160 km in 2 h = 80 km/h.

Electrical energy (bill units)

E (kWh)=P (kW)×t (h)E\,(\text{kWh}) = P\,(\text{kW}) \times t\,(\text{h})

1 unit on the bill = 1 kWh.

Profit percentage

Profit %=ProfitCost price×100\text{Profit}\,\% = \frac{\text{Profit}}{\text{Cost price}} \times 100

Profit = selling price − cost price. Bought for Rs 500, sold for Rs 600: profit = Rs 100, so profit % = 20%.

03Real World Examples

Budgeting at home

Families plan monthly spending on rent, bills, groceries and school fees: arithmetic and percentages.

Cooking for guests

A recipe for 4 people used for 12 means multiplying every ingredient by 3: ratio and proportion.

Mobile packages

Comparing data packages means working out the cost per GB to find the best deal.

Farming

Farmers calculate how much fertiliser per acre and water per field they need.

04Practice Questions

Try to answer in your own words first, then open the model answer.

Short questions

Q1.A bag costs Rs 3,200. It is sold at 15% off. Find the sale price.Show answer

Answer

  • Discount = 15 ÷ 100 × 3,200 = Rs 480
  • Sale price = 3,200 − 480 = Rs 2,720
Q2.A 100 W bulb is on for 10 hours. How many units of electricity does it use?Show answer

Answer

  • Power = 100 W = 0.1 kW
  • Energy = 0.1 kW × 10 h = 1 kWh = 1 unit
Q3.Ali scored 72, 85, 64 and 79 in four tests. Find his average.Show answer

Answer

  • Sum = 72 + 85 + 64 + 79 = 300
  • Average = 300 ÷ 4 = 75
Q4.A shopkeeper buys a fan for Rs 4,000 and sells it for Rs 4,600. Find his profit percentage.Show answer

Answer

  • Profit = 4,600 − 4,000 = Rs 600
  • Profit % = 600 ÷ 4,000 × 100 = 15%
Q5.Name four careers in which mathematics is essential.Show answer

Answer

  • Engineer
  • Chartered accountant
  • Actuary
  • Data scientist / statistician

(Software developer, banker, architect and economist are also correct.)

Long questions

Q6.Explain with examples how mathematics is used in daily life.Show answer

Answer

  1. Shopping: percentages for discounts. 25% off Rs 2,400 = Rs 600 saved.
  2. Bills: units of electricity. 1.5 kW × 8 h = 12 units.
  3. Travel: time = distance ÷ speed. 160 km at 80 km/h = 2 h.
  4. Cooking: ratio and proportion to scale recipes.
  5. Sports: averages, strike rates and run rates.
  6. Religious duties: Zakat at 2.5% of eligible savings.

05Quiz

Question 1 of 8
20% of Rs 1,500 is:

These topics connect to what you just learned.

In other subjects

In Mathematics