Choose an exam and explore concepts through visual explanations, topic maps and revision checks. Open the full chapter notes whenever you need more detail.
THE VISUAL LEARNING STUDIO
See the idea. Understand the connection.
35 visual explanations across 29 chapters, with topic maps throughout the library.
The chapter index will grow as additional notes are prepared. Chapters shown here are a learning collection, not a claim that the entire exam syllabus is complete.
SEE IT. CONNECT IT. EXPLAIN IT.
Understand the chapter visually
1 visual explanation · Study the connections, then test yourself.
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FOLLOW THE PROCESS
Successive percentages multiply
1
Choose a starting value
Use 100 if a convenient base is needed.
2
Apply the first factor
A 20% increase multiplies by 1.20.
3
Apply the next factor
A 20% decrease then multiplies the new value by 0.80.
4
Compare with the original
100 × 1.20 × 0.80 = 96: a net decrease of 4%.
The connection Each percentage change uses the value at that step as its base.
Exam trap Adding +20% and −20% ignores their different bases.
What happens after +10% followed by −10%?
Multiply 1.10 × 0.90 = 0.99, so the net change is a 1% decrease.
Study the expanded notes and the credited detailed textbook lessons. The current chapter index covers core topics; it is not a claim of exhaustive coverage of every examination syllabus. Check the official syllabus and primary references.
Percentages and Successive Changes — lesson overview
Meaning and conversion
A percentage is a fraction out of one hundred: x% = x/100. To find p% of a quantity, multiply that quantity by p/100.
Useful conversions: 1/2 = 50%; 1/4 = 25%; 1/5 = 20%; 1/8 = 12.5%; 3/4 = 75%. These are identities, not estimation rules.
An increase or decrease is measured relative to its stated base. Percentage change = change ÷ original value × 100.
Different bases produce different percentages
If a price rises from ₹80 to ₹100, the increase is ₹20 on a base of ₹80: 25%. If it then falls from ₹100 to ₹80, the decrease is 20% of ₹100.
The absolute change is the same ₹20, but the denominator differs. Therefore a rise and its reversal need not have the same percentage.
Percentage points compare percentage figures directly. Moving from 20% to 25% is an increase of five percentage points and a relative increase of 25%.
Successive changes: worked example
A 20% rise multiplies a value by 1.20. A 10% fall multiplies the new value by 0.90. Combined multiplier = 1.20 × 0.90 = 1.08.
Starting from ₹100, the final value is ₹108: an 8% net rise, not 10%. The second percentage applies to the changed base.
For signed changes a% and b%, net percentage change = a + b + ab/100. Use a negative sign for decreases.
