Ratio, Proportion & Alligation Mixtures
Practice 400+ official SSC CGL Ratio & Proportion PYQs online. Alligation rule, mean proportional, income-expenditure ratios & step-by-step solutions.
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4-Step Solution & Tricks
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🎯 High-Yield Syllabus Breakdown
These high-frequency concepts account for over 90% of all questions asked in Ratio, Proportion & Alligation Mixtures:
- Combining Ratios: a:b and b:c to a:b:c
- Mean Proportional b = √(ac) & Third Proportional c = b²/a
- Fourth Proportional d = bc / a
- Alligation Rule for Mixtures & Average Cost
- Income, Expenditure & Savings Ratios (Income = Exp + Savings)
⚡ Essential Formulas & Speed Shortcuts
Formulas and time-saving shortcuts to solve Ratio & Proportion questions in under 45 seconds:
Mean Proportional between a and c: b = √(a · c).
Alligation cross difference gives the exact mixing ratio of quantities.
In replacement formula: Final Liquid = Initial × (1 - x/C)ⁿ.
📖 Sample Solved Exam Questions
Preview authentic questions from this chapter with full step-by-step solutions:
💡 View Step-by-Step Solution & Answer
Correct Answer: 50000
- Step 1: Understand problem conditions and equations.
- Step 2: If we assume the number of tickets of category A be 3 x, category B be 2x and category C be 5x Total tickets = 3x + 2x + 5x = 10x Now, total amount collection from selling the tickets will be (3x × 1000) + (2x × 500) + (5x × 200) = 2.5 crore ⇒+ += ⇒ ⇒ 3000/1000 1000/25000000 5000/25000000 5000 xxx x x So, total tickets = 10x = 10 × 5000 = 50000 t
- Step 3: Evaluating gives verified answer: 50000.
⚡ Speed Tip: Verify intermediate calculations and units.
💡 View Step-by-Step Solution & Answer
Correct Answer: 2 : 1 : 6
- Step 1 (Concept & Property): Identify the governing quantitative arithmetic property.
- Step 2 (Given Setup): Formulate algebraic relations from given values: A : B = 2 : 1 A : C = 1 : 3 = 2 : 6 ∴ A : B : C = 2 : 1 : 6.
- Step 3 (Solving): Solving and evaluating directly confirms the verified value: 2 : 1 : 6.
- Step 4 (Speed Tip): Cross-verify options using unit digit or divisibility rules. Final Answer: 2 : 1 : 6.
⚡ Speed Tip: Cross-verify options using unit digit or divisibility rules.
💡 View Step-by-Step Solution & Answer
Correct Answer: 3 : 2
- Step 1: xy xx yy 33/22 5 1 − ++ = ⇒ −() ++() ++ = ⇒− = () xy xx yy xx yy xy 22/22 5 5 ...
- Step 2: i Again, xy xy 22 7− − = ⇒ +() −() − = ⇒+ = () xy xy xy xy 7 7 ....
- Step 3: ii On adding equations (i) and (ii), 2x = 12 ⇒ x = 6 From equation (ii), x+ y = 7 ⇒ y = 7 − 6= 1 ∴ 2 3/26 31 41x y = × × = :
⚡ Speed Tip: Verify intermediate calculations and units.
❓ Frequently Asked Questions (FAQs)
What is the Third Proportional to two numbers a and b?
Third Proportional c = b² / a. For example, third proportional to 4 and 12 is 12² / 4 = 144 / 4 = 36.