Ratio & Proportion – Quick Study Guide
(For Cisco CCNA – Quantitative Aptitude Section)
1. Simple Explanation
Ratio compares two or more quantities of the same unit.
- Notation: (a:b) or (a : b) or (\frac{a}{b}).
- Example: If 4 routers use 8 cables, the ratio of routers to cables is (4:8 = 1:2).
Proportion states that two ratios are equal.
- Notation: (\frac{a}{b} = \frac{c}{d}).
- Example: If the ratio of routers to cables is the same in two labs, then
(\frac{r_1}{c_1} = \frac{r_2}{c_2}).
In CCNA, ratios often appear in bandwidth calculations, network capacity planning, and cost‑benefit analyses.
2. Key Points
| Concept | What to Remember | Formula / Shortcut |
|---|---|---|
| Direct Proportion | (x) increases → (y) increases proportionally. | (y = kx) where (k) is the constant ratio. |
| Inverse Proportion | (x) increases → (y) decreases proportionally. | (y = \frac{k}{x}). |
| Cross‑Multiplication | To solve (\frac{a}{b} = \frac{c}{d}). | (a \times d = b \times c). |
| Finding Unknowns | Write the proportion with the unknown as a fraction. | (\frac{a}{b} = \frac{c}{x}) → (x = \frac{b \times c}{a}). |
| Unit Rate | Ratio expressed per one unit of the denominator. | ( \text{unit rate} = \frac{a}{b} ). |
| Scaling | Multiplying numerator and denominator by the same factor keeps the ratio unchanged. | ( \frac{a}{b} = \frac{ka}{kb}). |
| Percentage from Ratio | ( \text{percentage} = \frac{\text{part}}{\text{whole}} \times 100 ). | Convert ratio to fraction first. |
3. Worked Example (CCNA‑Style)
Problem
A network lab has 3 core switches that support 12 ports each.
In a new lab, the number of core switches is increased to 5, but the total number of ports must remain the same as the old lab.
How many ports should each switch in the new lab have?
Step‑by‑Step
-
Calculate total ports in old lab
[ \text{Total ports}_{old} = 3 \text{ switches} \times 12 \text{ ports/switch} = 36 \text{ ports} ] -
Set up proportion
Let (x) = number of ports per switch in the new lab.
[ \frac{3 \text{ switches}}{12 \text{ ports/switch}} = \frac{5 \text{ switches}}{x \text{ ports/switch}} ] -
Cross‑multiply
[ 3 \times x = 5 \times 12 \quad \Rightarrow \quad 3x = 60 ] -
Solve for (x)
[ x = \frac{60}{3} = 20 \text{ ports/switch} ]
Answer
Each new switch must have 20 ports.
4. Quick Revision Summary
| Topic | Formula | Quick Tip |
|---|---|---|
| Direct Proportion | (y = kx) | Remember “k” = constant ratio. |
| Inverse Proportion | (y = \dfrac{k}{x}) | As (x) grows, (y) shrinks. |
| Cross‑Multiplication | (a:d = b:c \Rightarrow a \times c = b \times d) | Always multiply outer by inner. |
| Unknown in Proportion | (\frac{a}{b} = \frac{c}{x} \Rightarrow x = \dfrac{b \times c}{a}) | Isolate the unknown on one side. |
| Unit Rate | (\frac{part}{whole}) | Express per one unit of the denominator. |
| Scaling | (\frac{a}{b} = \frac{ka}{kb}) | Multiply both numerator & denominator by same number. |
Final Thought
Mastering ratios and proportions gives you a powerful tool to quickly analyze network scaling, bandwidth distribution, and cost ratios—skills that are directly useful for CCNA exam questions and real‑world network design. Keep practicing with real‑life scenarios like the example above to build confidence!