Ratio and Proportion
- Formula / Rule
- Ratio and Proportion
- Topic
- Ratio & Proportion
- Formula
Ratio: $a : b = \frac{a}{b}$
Proportion: $a : b = c : d \implies ad = bc$ (cross multiplication)
Third proportional to $a, b$: $x = \frac{b^2}{a}$
Fourth proportional to $a, b, c$: $x = \frac{b \times c}{a}$
Mean proportional between $a$ and $b$: $x = \sqrt{ab}$
Componendo-Dividendo rule: If $a:b = c:d$, then $(a+b):(a-b) = (c+d):(c-d)$
- When to Use
- Dividing quantities in a given ratio, finding unknowns in proportions, and solving mixture problems.
- Worked Example
Q: Divide $540$ in the ratio $4:5$.
$\text{Total parts} = 4+5 = 9$ $\text{First part} = \frac{4}{9} \times 540 = 240$ $\text{Second part} = \frac{5}{9} \times 540 = 300$