Q1
School boys:girls ratio is 11:15. If 200 more girls join, find boys count.
Solution
Difference (15-11)=4 units → 200. 1 unit → 50. Boys = 11 × 50 = 550.
1. Basic Concepts (Flow Chart)
Part-11
Ratio Definition
Comparison between two quantities of the same type.
a : b
2
Duplicate Ratio
Square of the ratio.
a² : b²
3
Sub-duplicate Ratio
Square root of the ratio.
√a : √b
4
Triplicate Ratio
Cube of the ratio.
a³ : b³
Property of Ratios
a : b = aK : bK = (a/K) : (b/K).
2. Proportion Concepts (समानुपात)
Part-21
Basic Proportion
If a : b = c : d, they are in proportion.
ad = bc
2
Mean Proportional
Between a and b.
x = √(ab)
3
Third Proportional
Calculated for a and b.
x = b² / a
4
Fourth Proportional
Calculated for a, b, and c.
x = (bc) / a
3. Variations & Dependencies
Part 5-6V1
Direct & Inverse
Direct: x ∝ y | Inverse: x ∝ 1/y.
V2
Breaking Rule
Value depends on power of weight (Diamonds/Marble).
Cost ∝ (Weight)²
Solved Practice Problems
Complete CollectionQ2
A diamond breaks in ratio 1:2:3:4. Cost ∝ weight². Loss is Rs. 70,000. Find original price.
Solution
Initial weight 10². Broken weights sum (1²+2²+3²+4²)=30. Loss 70 units → 70,000. Original = Rs. 1,00,000.
Q3
A salary increased 8:11. If new salary is Rs. 33,000, what was original?.
Solution
11 units → 33,000. 1 unit → 3,000. Original 8 units = Rs. 24,000.
Q4
Income ratio A:B is 5:4, savings ratio 7:5. Each saves Rs. 4,800. Find income sum.
Solution
Applying cross product/normalization: Total sum = Rs. 21,120.