Ratio & Proportion – Tamil Nadu TET (Quantitative Aptitude)
Purpose:
Master the concept of ratio (comparative size) and proportion (equivalent ratios).
These are core to many TET questions – from simple “A : B = C : D” to mixture, time‑speed, and part‑of‑whole problems.
1. Simple Explanation
| Term | Definition | Symbol | Example |
|---|---|---|---|
| Ratio | A comparison of two quantities. | a : b |
4 : 5 |
| Proportion | Two ratios are equal. | a : b = c : d |
4 : 5 = 8 : 10 |
Key idea:
If two ratios are equal, then multiplying the first term of one ratio by the second term of the other ratio gives the same product as multiplying the second term of the first ratio by the first term of the other ratio.
Mathematically: a : b = c : d ⇔ a·d = b·c.
2. Key Points & Formulae
| Category | 📌 What to remember | Formula / Shortcut |
|---|---|---|
| Basic Ratio | Write as x : y or x/y. |
— |
| Equivalent Ratios | Multiply/divide both terms by same number. | x : y = (kx) : (ky) |
| Proportion Test | a:b = c:d → cross‑multiply. |
a·d = b·c |
| Finding Missing Term | a : b = c : ? → b·c = a·? |
? = (b·c)/a |
| Compound Ratio | Two ratios multiplied: (a:b)·(c:d). |
ac : bd |
| Part of a Whole | If x is y% of z, then x = (y/100)·z. |
z = (x·100)/y |
| Mixture/Weighted Average | Total = (a·p + b·q)/(a + b) where p,q = values, a,b = quantities. |
— |
| Time‑Speed‑Distance | Distance = Speed × Time. |
— |
| Rate of Change | Rate = (Change in Quantity)/(Change in Unit) |
— |
3. Worked Example
Question
The ratio of the ages of a father and son is 8 : 3. If the son is 9 years old, find the father’s age.
Step‑by‑Step
-
Set up the proportion
[ \frac{\text{Father}}{\text{Son}} = \frac{8}{3} ] Let father’s age = (F). -
Cross‑multiply to solve for (F)
[ 3F = 8 \times 9 \quad\Rightarrow\quad 3F = 72 ] -
Divide to isolate (F)
[ F = \frac{72}{3} = 24 ]
Answer
The father is 24 years old.
Another Example – Part of a Whole
Problem:
A jar contains 30 g of sugar. 20 % of the jar’s content is sugar. Find the total capacity of the jar.
- Let total capacity = (T).
- (20% \text{ of } T = 30) g → (\frac{20}{100}T = 30).
- Solve: (0.20T = 30) → (T = 150).
Answer: The jar holds 150 g in total.
4. Quick Revision Summary
- Ratio = comparison of two numbers (
x : y). - Proportion = equality of two ratios (
a:b = c:d). - Check a proportion by cross‑multiplying:
a·d = b·c. - Missing term in a proportion:
? = (b·c)/a. - Part of a whole:
xisy%ofz→z = (x·100)/y.
- Compound ratio:
(a:b)·(c:d) = ac : bd. - Mixture: Weighted average of values.
- Time‑Speed‑Distance:
D = S × T.
Tip: Always convert percentages to decimals (e.g., 20 % → 0.20) before calculation.
Tip: Use the cross‑multiplication shortcut to verify proportions quickly.
Quick Practice Question
The ratio of boys to girls in a class is 5 : 3. If there are 80 students, how many boys are there?
Answer (quick):
Total parts = 5 + 3 = 8.
One part = 80 / 8 = 10.
Boys = 5 × 10 = 50.
Use this structure to practice more problems and to solidify your understanding of ratios & proportions for the Tamil Nadu TET!