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Calculate a Given Percentage of a Quantity
To find a percentage of a number:
Practice Problem:
Find 25% of 640
Answer: 0.25 x 640 = 160
Express One Quantity as a Percentage of Another
To express A as a % of B, use:
Percentage Increase or Decrease
Formula:
Simple & Compound Interest
Simple Interest:
Compound Interest:
Multiply the new total each year by:
Reverse Percentages
Use when you know the result after a % increase/decrease, and want the original value.
Example: a price after a 20% increase is $120. What was the original?
Remember the formula we stated and replace what we don't know with an "x"
Profit/Loss
If a shop sells something above cost price → profit
If it sells below → loss
Selling price = Cost price + Profit. For example, if you buy a phone for $300 and sell it for $360, your profit is 360 - 300 = $60
Discount Formulas
To find the discount amount:
Discount = (Discount Percentage ÷ 100) × Original Price
To find the sale price (after the discount):
Sale Price = Original Price − Discount
OR (shortcut method): Sale Price = Original Price × (1 − Discount Percentage ÷ 100)
Practical Problem:
An item costs $80 and there’s a 25% discount. Find the sale price.
Discount amount = (25 ÷ 100) × 80 = $20
Sale Price = 80 − 20 = $60
Or using the shortcut:
Sale Price = 80 × (1 − 0.25) = 80 × 0.75 = $60
Time:
Example: how many seconds are there in 2 hours?
2 hours = 2 × 60 minutes = 120 minutes
120 minutes = 120 × 60 = 7,200 seconds
Practice Problem:
How many minutes are in 3.5 hours?
Answer: 3.5 × 60 = 210 minutes
12-Hour vs 24-Hour Clock
12-Hour Clock:
Uses AM (midnight to noon) and PM (noon to midnight)
Example: 7:00 PM is evening
24-Hour Clock:
Removes AM/PM; numbers go from 00:00 to 23:59
Midnight = 00:00
Noon = 12:00
7:00 PM = 19:00 (7 + 12)
3:15 AM = 03:15
3:15 PM = 15:15 (3+12)
Practice Problem:
Convert the following:
8:45 PM → ? and 04:10 → ?
Answer: 8:45 + 12:00 = 20:45 and 04:10 = 4:10 AM
Reading Clocks and Timetables
You’ll often be asked to:
Read departure/arrival times
Work out how long a journey takes
Plan around multiple stops
Example:
Train departs at 13:45 and arrives at 16:20. How long is the journey?
16:20 − 13:45. You can count forward from 13:45:
From 13:45 → 14:00 = 15 minutes. Keep this 15 minutes aside.
Now from 14:00 to 16:20 = 2 hours 20 minutes
Add them: 15 min + 2 hr 20 min = 2 hr 35 min
Time Zone Problems
Time zone questions often say something like:
A flight leaves Cairo at 11:00 AM local time to Dubai and takes 5 hours. Dubai is 2 hours ahead. What is the arrival time?
Steps:
Add flight time: 11:00 + 5h = 16:00
Add time difference (2 hours ahead):
→ 18:00 local time at destination
Practice Problem:
A flight leaves at 21:00 local time and lands 6 hours later. The destination is 3 hours behind. What time is it locally when the flight lands?
Answer: Add flight time: 21:00 + 6:00 = 27:00 - 24 = 03:00.
Subtract the time difference: 03:00 - 3 = 00:00 (midnight)
NOTES DONE BY FARIDA SABET
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