Percentage Comparison — More Than, Less Than & Base Value

The trickiest part of percentage questions is understanding which number is the base. The same two numbers produce different percentage answers depending on what's being asked.

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The Four Types of Percentage Questions

Given two quantities, there are exactly 4 things you can be asked:

Question Type	Formula	Base Value
A is what percent of B?	(A/B) × 100	B
B is what percent of A?	(B/A) × 100	A
A is how much percent more than B?	((A−B)/B) × 100	B
B is how much percent less than A?	((A−B)/A) × 100	A

Critical rule: The base value is always the one that comes after "of" or after "than".

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Example: Neha has 40 books, Pooja has 32 books

Ratio = Neha : Pooja = 40 : 32 = 5 : 4

Q1: Neha's books are what percent of Pooja's books?

• Base = Pooja = 4
• (5/4) × 100 = 125%

Q2: Pooja's books are what percent of Neha's books?

• Base = Neha = 5
• (4/5) × 100 = 80%

Q3: Neha's books are how much percent MORE than Pooja's?

• Difference = 1, Base = Pooja = 4
• (1/4) × 100 = 25%

Q4: Pooja's books are how much percent LESS than Neha's?

• Difference = 1, Base = Neha = 5
• (1/5) × 100 = 20%

Notice: "25% more" and "20% less" are different answers for the same two numbers. The base changes!

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Example: Ram's salary = Rs. 2125, Shyam's salary = Rs. 2975

Simplify: 2125 : 2975 → (2000+125) : (3000−25) → 85:119 → R : S = 5 : 7

Q1: Ram's salary is what percent of Shyam's?

• Base = Shyam = 7
• (5/7) × 100 = 71.43%

Q2: Shyam's salary is what percent of Ram's?

• Base = Ram = 5
• (7/5) × 100 = 140%

Q3: Ram's salary is what percent of total (Ram + Shyam)?

• Total = 5 + 7 = 12, Base = Total = 12
• (5/12) × 100 = 41.67%

Q4: Ram earns how much percent LESS than Shyam?

• Difference = 2, Base = Shyam = 7
• (2/7) × 100 = 28.57%

Q5: Shyam earns how much percent MORE than Ram?

• Difference = 2, Base = Ram = 5
• (2/5) × 100 = 40%

Q6: Difference is what percent of Ram's salary?

• Difference = 2, Base = Ram = 5
• (2/5) × 100 = 40%

Q7: By what percent should Ram's salary increase to equal Shyam's?

• Ram must go from 5 → 7, increase = 2
• Base = Ram (original) = 5
• (2/5) × 100 = 40%

Q8: By how much should Ram's salary increase to become 80% of Shyam's?

• 80% of Shyam = 80% × 2975 = 2380
• Increase needed = 2380 − 2125 = Rs. 255

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The Ratio Shortcut for "More/Less Than"

Once you simplify the ratio, finding "more than" or "less than" percentages is instant:

Ratio A : B	A is _% more than B	B is _% less than A
5 : 4	1/4 × 100 = 25%	1/5 × 100 = 20%
7 : 5	2/5 × 100 = 40%	2/7 × 100 = 28.57%
3 : 2	1/2 × 100 = 50%	1/3 × 100 = 33.33%
4 : 3	1/3 × 100 = 33.33%	1/4 × 100 = 25%
8 : 3	5/3 × 100 = 166.67%	5/8 × 100 = 62.5%

Pattern: For "more than", the difference goes over the smaller number. For "less than", the difference goes over the larger number.

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"By What Percent Should X Increase to Equal Y?"

This is a disguised "more than" question.

Example: A = 24, B = 64. By what % should A increase to become B?

• Ratio = 24 : 64 = 3 : 8
• Increase needed = 5 (from 3 to 8), Base = 3
• (5/3) × 100 = 166.67%

Example: Student 1 scored 84, Student 2 scored 105. By what % should 84 increase to become 105?

• 84 : 105 = 28 : 35 = 4 : 5
• Increase = 1, Base = 4
• (1/4) × 100 = 25%

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"What is the Difference as a Percent of the Smaller Quantity?"

Example: Quantities are 64 and 24.

• Ratio = 64 : 24 = 8 : 3
• Difference = 5, Base = smaller = 3
• (5/3) × 100 = 166.67%

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Rahul vs Amit

Rahul scored 72, Amit scored 90.

"Rahul's marks are how much percent less than Amit's?"

• 72 : 90 = 4 : 5
• Difference = 1, Base = Amit = 5
• (1/5) × 100 = 20%

Key takeaway: Always identify the base first. The word after "of" or "than" tells you the base. Get this right and you'll never make a percentage comparison mistake.