Alligation Cross: Draw an X. Put cheaper on top-left, dearer on bottom-left, mean in center. Cross-subtract to get the ratio of quantities.
Ratio & Proportion Shortcuts
SBI POIBPS POSSC CGLRRB
Items to Memorize
- If a:b = 2:3, actual values = 2k and 3k
- Componendo-Dividendo: if a/b = c/d then (a+b)/(a−b) = (c+d)/(c−d)
- Chain Rule: link ratios by making common term equal
- Mixture: use alligation cross method
- Partnership: Profit ratio = Capital × Time ratio
- Dividing in ratio: A's share = A/(A+B+C) × Total
- Duplicate ratio of a:b = a²:b²
- Sub-duplicate ratio of a:b = √a:√b
- Mean proportional of a and b = √(ab)
- Third proportional to a,b = b²/a
Mnemonic Tricks
How It Maps
| Cue | Maps To |
|---|---|
| Top-left | Cheaper price (or lower concentration) |
| Center | Mean price (or desired concentration) |
| Bottom-left | Dearer price (or higher concentration) |
| Top-right | Dearer − Mean (quantity of cheaper) |
| Bottom-right | Mean − Cheaper (quantity of dearer) |
Why It's Faster
The alligation method solves mixture, partnership, and average problems visually without equations. One technique covers 5+ question types in banking exams.
Frequently Asked Questions
What is the alligation method?
Alligation is a visual cross-multiplication method to find the ratio in which two quantities at different prices/concentrations must be mixed to get a desired mean. Draw an X, place values, cross-subtract.
How to solve partnership problems quickly?
Profit sharing ratio = (Capital₁ × Time₁) : (Capital₂ × Time₂). If times are equal, ratio is simply Capital₁ : Capital₂.
What is componendo-dividendo?
If a/b = c/d, then (a+b)/(a−b) = (c+d)/(c−d). This shortcut is useful when you know the ratio and need sum/difference relationships.