■ Ratio & Proportion Formula Sheet — Quick
Shortcuts
1. Basic Ratio Formula
If two quantities a and b are in the ratio m:n, then:
a = (m / (m + n)) × T and b = (n / (m + n)) × T, where T = a + b.
2. Direct Proportion
If (u / v) = k, then: u = kv and v = u / k.
3. Chain Proportion (Shortcut Trick)
If (u / v) = (v / w) = k, then simply follow the chain:
w × k → v × k → u
Therefore, u = w × k².
4. Inverse Proportion
If (u × v) = k, then: u = k / v and v = k / u.
Shortcut: If one quantity doubles, the other halves.
5. Compound Proportion
If (u / v) = (v / w) = (w / x) = k, then:
u = x × k³.
Rule: Count the jumps between first and last variable, multiply by k that many times.
6. Mixing Ratio Problems
If two items A and B are mixed in the ratio m:n, then the price = (m × PA + n × PB) / (m + n), where
PA and PB are prices of A and B.
7. Golden Shortcut Table
Given Formula
a / b = k a = k × b
a / b = b / c = k a = c × k²
a / b = b / c = c / d = k a = d × k³
