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Number - Time and Money Calculations

Grade 9IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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12-hour and 24-hour clock systems: Converting between AM/PM and the 00:00-23:59 format.

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Time intervals: Calculating the duration between two events, often crossing midnight or involving different time zones.

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Currency conversion: Using exchange rates to convert between different currencies (Multiplication/Division).

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Simple Interest: Interest calculated only on the initial principal amount.

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Compound Interest: Interest calculated on the principal plus any accumulated interest from previous periods.

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Profit and Loss: Calculating percentage increases or decreases based on cost and selling prices.

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Earnings: Understanding gross pay, net pay, and basic deductions like tax.

📐Formulae

SimpleInterest(I)=P×R×T100Simple Interest (I) = \frac{P \times R \times T}{100} where PP is principal, RR is rate, and TT is time in years.

TotalAmount(CompoundInterest)(A)=P(1+r100)nTotal Amount (Compound Interest) (A) = P(1 + \frac{r}{100})^n where nn is the number of years.

Percentage Profit/Loss=Actual Profit/LossCost Price×100\text{Percentage Profit/Loss} = \frac{\text{Actual Profit/Loss}}{\text{Cost Price}} \times 100

Exchange Rate Calculation:Value in Currency B=Value in Currency A×Exchange Rate\text{Exchange Rate Calculation}: \text{Value in Currency B} = \text{Value in Currency A} \times \text{Exchange Rate}

💡Examples

Problem 1:

A flight leaves London at 22:15 on Tuesday and arrives in Dubai at 08:40 on Wednesday. The local time in Dubai is 4 hours ahead of London. Calculate the total duration of the flight.

Solution:

  1. Convert arrival time to London time: 08:40 - 4 hours = 04:40 (Wednesday).
  2. Calculate time from 22:15 to midnight: 1 hour 45 minutes.
  3. Calculate time from midnight to 04:40: 4 hours 40 minutes.
  4. Total duration: 1h 45m + 4h 40m = 6 hours 25 minutes.

Explanation:

To find the duration, normalize both times to the same time zone first, then calculate the elapsed time across the midnight boundary.

Problem 2:

Calculate the total amount in a savings account after 3 years if $5000 is invested at a compound interest rate of 4% per year.

Solution:

  1. Use formula A=P(1+r100)nA = P(1 + \frac{r}{100})^n
  2. A=5000(1+4100)3A = 5000(1 + \frac{4}{100})^3
  3. A=5000(1.04)3A = 5000(1.04)^3
  4. A=5000×1.124864=5624.32A = 5000 \times 1.124864 = 5624.32

Explanation:

Apply the compound interest formula directly. Ensure the power nn corresponds to the number of years and the decimal multiplier reflects the percentage increase.

Problem 3:

A shopkeeper buys a laptop for 600andsellsitfor600 and sells it for 750. Calculate his percentage profit.

Solution:

  1. Profit = 750−750 - 600 = $150.
  2. Percentage Profit = 150600×100\frac{150}{600} \times 100.
  3. 14×100=25%\frac{1}{4} \times 100 = 25\%.

Explanation:

First, find the absolute profit by subtracting the cost price from the selling price. Then, divide the profit by the original cost price (not the selling price) and multiply by 100.