RRB NTPC Preparation Series: Part 6 - Ratio & Proportion in Maths

 

RRB NTPC Preparation Series: Part 6 - Ratio & Proportion in Maths 

Friends! Ee RRB NTPC 2025 preparation series lo Part 6 ki vacham, topic "Ratio & Proportion" meeda. Idi Maths lo foundation + high weightage chapter –

• CBT 1 lo 2-4 questions (7-13% weightage),
• CBT 2 lo 3-5 questions (9-14% weightage),
• Total Maths lo ~30% questions (with Time & Work, Interest, Percentage, Time & Distance combine).

2025 Update (Oct 28): RRB UG notification live – total vacancies 11,910. Ratio lo mixture, partnership, ages, sharing, direct/indirect proportion ekkuva vastunnayi. Proportion lo continued proportion, mean proportional, compound ratio trending. Exam Jan-Feb 2026.

• Formulas (20+)
• Shortcuts (10+)
• Examples (7 NTPC level)
• Practice (15 graded)
• Integration with Part 1-5
• 2025-specific strategy

Next Part 7: Mensuration? Adigite cheptha. Let’s conquer Maths 38+ marks! 💪

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Step 1: Introduction & NTPC Relevance

Friends, Ratio ante "2 quantities entha relation lo unnai", Proportion ante "2 ratios equal unte".

Sub-Topic	CBT 1 Qs	CBT 2 Qs	% Weightage
Basic Ratio	1	1	3-5%
Partnership	0-1	1	3-5%
Ages	0-1	1	3-5%
Mixture	0-1	1	3-5%
Total	2-4	3-5	12-14%

Telugu: Ee topic Time & Work (Part 4) lo efficiency, Profit & Loss (Part 2) lo sharing, Percentage (Part 1) lo conversion – backbone. English: Ratio = division, Proportion = equality. Master for 100% accuracy.

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Step 2: Core Concepts (Building Blocks)

Term	Telugu Meaning	English
Ratio (a:b)	a ni b tho compare	a/b
Proportion (a:b = c:d)	2 ratios equal	a/b = c/d
Direct Proportion	Ekam badithe inkokati kuda baduthundi	↑↑
Indirect/Inverse	Ekam badithe inkokati tagguthundi	↑↓
Continued Proportion	a:b = b:c	a/b = b/c
Mean Proportional	b² = a×c	√(a×c)

Telugu: 2:3 ante 2 parts A, 3 parts B. LCM use chey for actual values. English: a:b = c:d → a×d = b×c (cross multiply).

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Step 3: All Key Formulas (20+ with Telugu)

#	Formula	Telugu	Example
1	a:b = m:n → a/m = b/n	Ratio divide	4:6 = 2:3
2	a:b = c:d → a×d = b×c	Cross multiply	2:3 = 4:6 → 12=12
3	Divide in ratio m:n	Total = m+n parts	500 in 3:2 → 300:200
4	Partnership (Investment)	Profit = Investment × Time	A:B = 3:2
5	Ages ratio	Current = given, future/past = ±diff	5:3, diff 10 → 25:15
6	Mixture (Alligation)	(C1 - C2) : (Cm - C2) = Q2 : Q1	Milk:Water
7	Mean Proportional	√(a×c)	√(16×36)=24
8	Continued Proportion	b² = a×c	Same
9	Compound Ratio	(a×c×e):(b×d×f)	2:3 × 4:5 = 8:15
10	Direct Proportion	y = kx	Speed ↑, Time ↓
11	Inverse Proportion	y = k/x	Men ↑, Days ↓
12	A:B:C = x:y:z	LCM method	2:3:5 → 30 units
13	Increase/Decrease %	(new-old)/old ×100	Part 1 link
14	Partnership sleep	Profit after join	Standard
15	Ages after t years	Current + t	5:3 + 5 = 10:8
16	Mixture removal	Remaining = (1 - r)^n	Repeated
17	Duplicate/Triplicate	(a/b)^2 or ^3	Ratio square
18	Fourth Proportional	d = (b×c)/a	If a:b = c:d
19	Third Proportional	c = b²/a	If a:b = b:c
20	Component Ratio	a = x+y, b = x+z	Solve equations

English: Alligation = shortcut for mixture. LCM = total parts.

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Step 4: Shortcuts & Hacks (NTPC Speed Boosters)

#	Shortcut	Use
1	LCM of ratio numbers = total parts	3:4:5 → LCM=60
2	Alligation: (CP1-CP2) = Q2:Q1	Direct ratio
3	Ages: diff = ratio diff × actual	5:3 diff 2 → actual diff 10
4	Partnership: Profit = Inv × Time	Ratio
5	Inverse: multiply ratios	Men:Days = 1/ratio
6	Mean: √(a×c)	Quick
7	Divide: part = (m/(m+n)) × total	Direct
8	Mixture: cost = weighted avg	Alligation
9	Compound: multiply ratios	2:3 × 4:5
10	Cross multiply = check	a×d = b×c

Telugu: Alligation 5 secs lo solve. English: Memorize alligation & LCM.

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Step 5: Step-by-Step Examples (7 NTPC Level)

Example 1 (Basic Ratio - CBT 1) Q: Divide Rs. 1200 in 3:5. Shares? Step 1: Total parts = 8 Step 2: 1 part = 1200/8 = 150 Step 3: A = 3×150 = 450, B = 750

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Example 2 (Ages - CBT 2) Q: A:B age 5:3, diff 20 yrs. Present ages? Step 1: Ratio diff = 2 parts = 20 yrs Step 2: 1 part = 10 Step 3: A = 50, B = 30

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Example 3 (Partnership - 2025 Trend) Q: A invests 6000 for 4 months, B 8000 for 6 months. Profit 5000. A’s share? Step 1: A = 6000×4 = 24000, B = 8000×6 = 48000 Step 2: Ratio 24:48 = 1:2 Step 3: A = (1/3)×5000 = 1666.67

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Example 4 (Mixture Alligation) Q: Milk 20/l, Water 5/l. Mix in 3:2 to get 14/l. Ratio? Step 1: CP1=20, CP2=5, Cm=14 Step 2: (20-14):(14-5) = 6:9 = 2:3

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Example 5 (Inverse Proportion) Q: 6 men do in 10 days. 15 men in how many? Step 1: Men × Days = constant Step 2: 6×10 = 15×D → D = 4 days

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Example 6 (Continued + Mean - Hard) Q: a:b = b:c = 2:3. If a=8, find c? Mean proportional? Step 1: b² = a×c → b² = 8×c Step 2: a:b=2:3 → 8:b=2:3 → b = 12 Step 3: 12² = 8×c → c = 18 Step 4: Mean = √(8×18) = 12

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Example 7 (Mixture Removal - Tricky 2025) Q: Vessel 60L milk. 10L removed, water added. Repeated 3 times. Remaining milk? Step 1: Fraction remaining = (1 - 10/60)³ = (5/6)³ = 125/216 Step 2: Milk = 60 × 125/216 = 34.72 L

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Step 6: Practice Questions (15 Graded)

Easy

1. 4:5 = ?:20
2. Divide 900 in 2:3:4

Medium 3. A:B = 3:4, B:C = 5:6. A:C? 4. 8 men do in 15 days. 12 men in? 5. Ages 7:5, diff 12. Younger?

Hard 6. A:B:C invest 3:4:5. Profit 12000. C’s share? 7. Rice 40/kg, 50/kg. Mix 3:2 for 46/kg. Ratio? 8. A:B age 5:3. After 6 yrs 7:5. Present? 9. 500 coins in 3:4:5. Total value if 1:2:3 paise? 10. Milk 60L, remove 1/3, add water. Repeated twice. Milk left? 11. A:B = 2:3, B:C = 4:5. A:B:C? 12. Partnership: A 12000×12, B 15000×8, C joins last 4 months 10000. Profit 4400. C’s share? 13. Mean proportional of 12 and 48? 14. 4 numbers in proportion. First 3 are 2,3,6. Fourth? 15. A does work in ratio 3:4 with B. Together 12 days. A alone?

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Step 7: Answers + Explanations

1. 16
2. 200:300:400
3. 15:22
4. 10 days
5. 30
6. 5000
7. 1:1
8. 24:14.4
9. Rs. 720
10. 26.67 L
11. 8:12:15
12. 400
13. 24
14. 9
15. 20 days

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Step 8: 2025 Strategy + Common Mistakes

Strategy:

• Daily: 50 questions (RS Aggarwal Ch. 6-7).
• Alligation Chart: Draw for mixture.
• Mock: PracticeMock 2025 – Ratio section.
• Link: Ratio = Efficiency (Part 4), % (Part 1), Sharing = Profit (Part 2).

Avoid:

• Cross multiply miss.
• Inverse forget.
• LCM skip in divide.