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SSC CGL Preparation – Day 14
Quantitative Aptitude: Ratio and Proportion (Repeated)
📘 SSC CGL Quantitative Aptitude – Complete Theory + Tricks + Examples
1. Ratio – Definition & Concepts
Definition:
A ratio is a relationship between two quantities, showing how many times one value contains or is contained in the other.
General Form:
If two numbers are a and b, their ratio is written as a : b and read as “a is to b”.
Important Points:
- Ratios are always expressed in simplest form.
- They have no units.
- Multiply or divide both terms by the same number → ratio remains unchanged.
Example:
If the ratio of boys to girls is 4:5, and total students are 90,
⇒ 4x + 5x = 90 ⇒ x = 10
⇒ Boys = 40, Girls = 50
2. Proportion – Definition & Concepts
Definition:
A proportion is an equation that states two ratios are equal.
General Form:
a : b :: c : d (read as “a is to b as c is to d”)
⇒ a/b = c/d
⇒ Product of extremes = Product of means ⇒ a × d = b × c
3. Types of Proportion
a) Direct Proportion
If two quantities increase or decrease together in the same ratio.
e.g., More men → More work done.
b) Inverse Proportion
If one quantity increases, the other decreases in inverse ratio.
e.g., More workers → Less time required.
4. Continued Proportion
If a/b = b/c, then a, b, c are in continued proportion.
⇒ b² = a × c
Example: Find the third proportional to 4 and 8.
Let x = third proportional ⇒ 4 : 8 = 8 : x ⇒ 4x = 64 ⇒ x = 16
5. Important Shortcuts & Tricks
🔹 Trick 1: Ratio of Two Numbers
If A/B = m/n, then A = m×x and B = n×x
🔹 Trick 2: New Ratio After Increment/Decrement
If a quantity is increased by x%, then
New quantity = Original × (1 + x/100)
Use for successive ratio problems.
🔹 Trick 3: Conversion of Ratios into Quantities
If total = T and ratio = a : b ⇒ A = T × (a / (a + b))
6. Problems on Ratio and Proportion (SSC Patterns)
🧠 Example 1:
Divide ₹1800 in the ratio 5:7.
→ Total parts = 5 + 7 = 12
→ Shares: ₹750 and ₹1050
🧠 Example 2:
The ratio of the ages of A and B is 3:5. After 10 years, the ratio will be 5:7. Find their current ages.
→ Let present ages = 3x and 5x
→ After 10 years:
(3x + 10)/(5x + 10) = 5/7
Cross-multiply & solve:
21x + 70 = 25x + 50 ⇒ x = 5
⇒ A = 15, B = 25
🧠 Example 3:
If a:b = 2:3, b:c = 4:5, find a:c?
→ Multiply corresponding terms:
a:b = 8:12, b:c = 12:15 ⇒ a:c = 8:15
7. Advanced Problems
🧠 Example 4:
A sum of money is divided among A, B, and C in the ratio 2:3:5. If C gets ₹400 more than A, find the total amount.
→ Ratio difference between C and A = 5 – 2 = 3 parts = ₹400
→ 1 part = ₹400 / 3 = ₹133.33
→ Total = (2+3+5) parts = 10 × ₹133.33 = ₹1333.30
8. SSC CGL Specific Tips
- Focus on solving age problems, income-expenditure, partnership, and mixture problems using ratio/proportion logic.
- Be comfortable with chain rule and comparison of ratios.
- Keep shortcuts memorized and use tables to convert % to ratios and vice versa.
9. Quick Reference Table: Percentage ↔️ Ratio
| Percentage | Ratio Form |
|---|---|
| 25% | 1 : 3 |
| 50% | 1 : 1 |
| 66.66% | 2 : 1 |
| 75% | 3 : 1 |
| 80% | 4 : 1 |
| 20% | 1 : 4 |
| 40% | 2 : 3 |
📝 Summary
| Topic | Key Formula / Idea |
|---|---|
| Ratio | a : b = a/b |
| Proportion | a/b = c/d ⇒ ad = bc |
| Continued Proportion | b² = ac |
| Third Proportional | a : b = b : x ⇒ x = b²/a |
| Fourth Proportional | a : b = c : x ⇒ x = (b × c)/a |
| Total Division in Ratio | T × (a / (a + b)) |
