Ratio & Proportion
Solve comparison problems instantly.
Core Concepts
A ratio compares two quantities (a:b). A proportion says two ratios are equal (a:b :: c:d).
Rule of Three
If a:b :: c:d, then a × d = b × c.
Product of Extremes = Product of Means.
Useful for finding missing values!
Splitting Quantities
To split a number N in ratio a:b:
1. Find total parts (a+b).
2. Value of 1 part = N / (a+b).
3. Multiply by a and b.
Solved Examples
Example 1: 3:5 :: 12:x
Question: Find x.
• 3 to 12 is ×4.
• So 5 to x must be ×4.
• 5 × 4 = 20.
• Answer: 20.
Example 2: Split 500 in 2:3
Question: Find the parts.
• Total parts = 2 + 3 = 5.
• 1 part = 500 / 5 = 100.
• Parts are 2×100 and 3×100.
• Answer: 200, 300.
Example 3: A:B=2:3, B:C=4:5
Question: Find A:B:C.
• B is 3 in first, 4 in second.
• LCM of 3 and 4 is 12.
• Multiply first ratio by 4: 8:12.
• Multiply second ratio by 3: 12:15.
• Answer: 8:12:15.
