चाल-दूरी-समय, कार्य और अनुपात: RAS गणित शॉर्टकट

Quantitative aptitude remains one of the most critically neglected yet high-scoring sections in RAS (Rajasthan Administrative Services) Prelims preparation. While most aspirants focus extensively on General Studies, the quantitative aptitude time distance speed work rate section can deliver 15-25 marks in the actual exam—marks that directly impact merit ranking. This comprehensive guide breaks down the three most tested problem types with exam-aligned strategies for the RAS 2026 cycle.

The RAS Prelims paper, conducted by the Rajasthan Public Service Commission (RPSC), allocates specific weightage to mathematical reasoning and quantitative problem-solving. Unlike banking or SSC exams where quant occupies 25-30% of the paper, RAS Prelims treats quantitative aptitude as an embedded reasoning component within the General Aptitude and Reasoning section. This makes mastery of core topics—quantitative aptitude time distance speed, work rate, and ratio proportion—essential for competitive scoring.

Understanding RAS Prelims Quantitative Aptitude Structure

Exam Pattern and Weightage (RAS 2026 Cycle)

The RAS Prelims exam is a single objective paper, "General Knowledge & General Science," comprising 150 questions carrying 200 marks, with a duration of 3 hours. Reasoning and quantitative-type questions are embedded within this single paper rather than forming a separate section; based on RajStudy's own analysis of the seven RAS Prelims papers actually held, Reasoning + Maths together have averaged around 21 questions per paper.

Understanding this weightage is crucial: improving your accuracy in quantitative aptitude can meaningfully move your rank, since Prelims is qualifying-only but every extra correct answer reduces your risk from negative marking.

Quick Formula Reference

Time-Distance-Speed Problems: Core Concepts and Strategies

Fundamental Formulas and Their RAS Application

Quantitative aptitude time distance speed problems test your ability to manipulate the relationship: Speed = Distance / Time.

The three core variants you'll encounter in RAS Prelims are:

1. Linear Motion Problems — Objects moving in straight lines
2. Relative Speed Problems — Two objects moving toward/away from each other
3. Circular Motion Problems — Objects on circular tracks

Linear Motion: Step-by-Step Solution Methodology

Example Problem (RAS-level): A train travels 240 km at 60 km/h for the first half of the distance, and 80 km/h for the remaining half. Calculate the average speed for the entire journey.

Solution Breakdown:

• Distance 1 = 120 km at 60 km/h → Time 1 = 120/60 = 2 hours
• Distance 2 = 120 km at 80 km/h → Time 2 = 120/80 = 1.5 hours
• Total Distance = 240 km
• Total Time = 2 + 1.5 = 3.5 hours
• Average Speed = 240 ÷ 3.5 = 68.57 km/h

Critical RAS Insight: Examiners frequently test the misconception that average speed is simply the arithmetic mean of two speeds. Always use: Average Speed = Total Distance ÷ Total Time.

Relative Speed: When Two Objects Move Simultaneously

When two objects move toward each other, relative speed = Speed₁ + Speed₂. When two objects move in the same direction, relative speed = |Speed₁ - Speed₂|.

1. Moving toward each otherRelative speed = Speed1 + Speed2; distance closes
2. Moving in the same directionRelative speed = |Speed1 - Speed2|; faster one catches up
3. Moving apart (opposite directions)Relative speed = Speed1 + Speed2; gap widens

Example Problem (RAS-Prelims 2023 pattern): Train A (90 km/h) and Train B (110 km/h) start from opposite ends of a 400 km track simultaneously. After how many hours will they meet?

Solution:

• Relative Speed = 90 + 110 = 200 km/h
• Time to Meet = 400 ÷ 200 = 2 hours

Circular Motion: Meeting and Overtaking on a Circular Track

On a circular track, two runners starting together meet for the first time (moving in opposite directions) after time = Track Length ÷ (Speed₁ + Speed₂), and one runner overtakes the other (moving in the same direction) after time = Track Length ÷ (Speed₁ - Speed₂).

Example Problem: Two runners start together on a 600 m circular track, one at 8 m/s and the other at 10 m/s, moving in the same direction. After how long will the faster runner lap the slower one?

Solution:

• Relative Speed (same direction) = 10 - 8 = 2 m/s
• Time to lap once = 600 ÷ 2 = 300 seconds = 5 minutes

Relative speed problems — linear, opposite-direction or circular-track — frequently connect to algebraic equation-solving in RAS question papers, so practising the equation-setup step pays off across all three variants.

Work Rate Problems: Breaking Down Efficiency-Based Challenges

Work Rate Fundamental Principle

The work rate approach is central to quantitative aptitude success in RAS. The core principle: If person A completes work in X days, A's work rate = 1/X per day.

Single Agent Work Problems

Example: Worker A completes a task in 12 days. Worker B completes it in 18 days. If they work together, how many days to complete the task?

Solution:

• A's rate = 1/12 per day
• B's rate = 1/18 per day
• Combined rate = 1/12 + 1/18 = (3+2)/36 = 5/36 per day
• Time to complete = 36/5 = 7.2 days = 7 days 4.8 hours

Multi-Agent Work with Efficiency Variations

RAS Prelims often complicates work problems by introducing efficiency multipliers or partial work scenarios.

Example Problem (Advanced): Worker A can complete a job in 20 days. Worker B is 25% more efficient than A. If they work together for 5 days, then A leaves and B continues alone, how many more days does B need?

Solution:

• A's rate = 1/20 per day
• B's efficiency = 125% of A = 1/20 × 1.25 = 1/16 per day
• Work completed in 5 days = 5 × (1/20 + 1/16) = 5 × (4+5)/80 = 45/80 = 9/16
• Remaining work = 1 - 9/16 = 7/16
• Days for B alone = (7/16) ÷ (1/16) = 7 days

This problem type frequently appears in RAS papers combined with time-distance-speed scenarios (e.g., workers traveling to a site and working simultaneously).

Ratio and Proportion: Foundation for All Quantitative Aptitude

Simplifying Complex Ratio Problems

Ratio problems in RAS Prelims test your ability to chain proportions and handle inverse relationships.

Definition: If A:B = m:n and B:C = p:q, then A:B:C = (m×p):(n×p):(n×q).

Practical RAS Application: Distribution and Mixture Problems

Example Problem: Three people invest in a business in the ratio 2:3:5. Annual profit is ₹50,000. Calculate each person's share.

Solution:

• Total parts = 2 + 3 + 5 = 10
• Person 1's share = (2/10) × 50,000 = ₹10,000
• Person 2's share = (3/10) × 50,000 = ₹15,000
• Person 3's share = (5/10) × 50,000 = ₹25,000

Verification: 10,000 + 15,000 + 25,000 = 50,000 ✓

Advanced Ratio Problems: Work and Efficiency

When combined with work rate concepts, ratio problems become significantly harder—but these are precisely the types RPSC tests.

Example Problem (RAS-level difficulty): Two workers complete a job in time ratio 3:4 (faster worker:slower worker). If the faster worker works for 6 days and the slower worker works for 8 days, they complete only 75% of the job. How many days does the faster worker need to complete the entire job alone?

Solution:

• Let faster worker complete job in 3x days; slower in 4x days
• Faster worker's rate = 1/(3x); Slower worker's rate = 1/(4x)
• Work done: 6/(3x) + 8/(4x) = 2/x + 2/x = 4/x = 0.75
• Therefore: x = 4/0.75 = 5.33 days
• Faster worker alone needs: 3 × 5.33 = 16 days

These complex ratio problems develop the logical reasoning skills essential for RAS's quantitative-reasoning questions.

Integrated Problem-Solving: Combining All Three Concepts

RAS Prelims frequently presents questions requiring knowledge of all three domains. Here's an authentic integration example:

Complex Example Problem: Three workers (A, B, C) work on a construction project. A can complete it in 30 days, B in 40 days, and C in 60 days. They work together for 5 days, then A leaves. B and C continue for 3 days, then C leaves and B continues alone. (a) How much work remains? (b) How many more days does B need alone? (c) What is the ratio of work completed by each person?

Solution:

• A's rate = 1/30; B's rate = 1/40; C's rate = 1/60
• Phase 1 (5 days, all three): Work = 5(1/30 + 1/40 + 1/60) = 5(4+3+2)/120 = 45/120 = 3/8
• Phase 2 (3 days, B & C): Work = 3(1/40 + 1/60) = 3(3+2)/120 = 15/120 = 1/8
• Remaining work: 1 - 3/8 - 1/8 = 4/8 = 1/2
• Days for B alone: (1/2) ÷ (1/40) = 20 days
• Ratio of work:
  • A: 5 × 1/30 = 1/6
  • B: 5 × 1/40 + 3 × 1/40 + 20 × 1/40 = 28/40 = 7/10
  • C: 5 × 1/60 + 3 × 1/60 = 8/60 = 2/15
  • Ratio = 1/6 : 7/10 : 2/15 = 5:21:4 (LCM method)

This complexity level reflects actual RAS Prelims questions from 2023-24.

Strategic Preparation Approach for the RAS 2026 Cycle

Time Allocation Strategy

The RAS Prelims paper gives you 3 hours for 150 questions — an average of 72 seconds per question across the whole paper. Quant questions typically need 60-90 seconds each to solve carefully, so budget accordingly:

1. Attempt only high-confidence questions (2-3 from each topic)
2. Skip trap questions quickly to preserve time
3. Master calculation speed through practice with elimination

Common Pitfalls RAS Aspirants Make

Exam-Specific Resources and Practice

The RPSC officially publishes past question papers at rpsc.rajasthan.gov.in. Note that RAS Prelims has not been held every year — real papers exist for 2013, 2015, 2016, 2018, 2021, 2023 and 2024 (held February 2025); there was no RAS Prelims exam in 2022 (or in 2014, 2017, 2019, 2020), so no genuine "2022 paper" exists to analyse. Work through the real papers from 2021, 2023 and 2024 for an authentic sense of how time-distance-speed, work rate and ratio questions are framed.

Key Takeaways

• Quantitative aptitude time distance speed, work rate, and ratio proportion account for 15-25 marks in RAS Prelims—a high-ROI subject for merit ranking improvement
• Master the three core time-distance-speed variants: linear motion, relative speed, and circular motion; avoid the average speed misconception
• Work rate problems demand precise formula application: combined rate = sum of individual rates; verify efficiency multipliers carefully
• Ratio proportion questions in RAS integrate with work/investment problems: practice chaining ratios and solving for unknowns systematically
• Integrated problem-solving is non-negotiable: practice multi-concept questions combining all three domains, as these reflect authentic RAS Prelims difficulty levels

Frequently Asked Questions

Q: How much weight does quantitative aptitude carry in RAS Prelims? A: Quantitative aptitude comprises approximately 15-25 marks (7.5-12.5%) of the 200-mark RAS Prelims paper. While not the largest section, these marks are often the difference between qualifying and not qualifying, as they test logical reasoning ability that correlates with administrative aptitude.

Q: What is the most commonly tested topic in RAS quantitative aptitude? A: Time-distance-speed, work rate and ratio-proportion all appear regularly across the real RAS Prelims papers (2021, 2023, 2024), without any one topic dominating heavily. Rather than preparing by a fixed percentage split, practise all three thoroughly and focus extra time on the integrated, multi-concept questions, since these are the ones aspirants most often lose marks on.

Q: Should I attempt all quantitative aptitude questions in the actual RAS Prelims exam? A: No. Given negative marking of 1/3 per wrong answer and the section's difficulty level, selective attempts are optimal. Attempt only 5-7 questions you're 85%+ confident on, rather than all 10-12, to protect your score from negative markings that disproportionately impact final merit ranking.

Practice Questions

1. Two trains depart from opposite ends of a 360 km track. Train A travels at 80 km/h and Train B at 100 km/h. A cyclist starts from Train A's starting point at the same time and travels toward Train B at 40 km/h. By the time the two trains meet each other, how many kilometers has the cyclist traveled?

a) 120 km
b) 90 km
c) 80 km
d) 110 km

Answer: c) 80 km

Explanation: The two trains move toward each other, so time taken for them to meet = 360 ÷ (80+100) = 360 ÷ 180 = 2 hours. In this same time, the cyclist, moving at 40 km/h, covers 40 × 2 = 80 km.

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2. Workers P and Q can complete a job in 18 days and 24 days respectively. They work together for 6 days, then P leaves. Q continues for 4 more days. How much work remains?

a) 1/4
b) 1/3
c) 5/12
d) 7/36

Answer: a) 1/4

Explanation: P's rate = 1/18; Q's rate = 1/24. Work in 6 days (both) = 6(1/18 + 1/24) = 6(4+3)/72 = 42/72 = 7/12. Work in next 4 days (Q only) = 4 × 1/24 = 4/24 = 1/6 = 2/12. Total work done = 7/12 + 2/12 = 9/12 = 3/4. Remaining work = 1 - 3/4 = 1/4.

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3. Three partners invest in a startup in the ratio 5:7:8. If the total investment is ₹60,000 and the annual profit is ₹30,000, what is Partner 2's share of profit (in ₹)?

a) ₹10,500
b) ₹11,000
c) ₹12,000
d) ₹9,500

Answer: a) ₹10,500

Explanation: Total ratio parts = 5+7+8 = 20. Partner 2's share of profit = (7/20) × 30,000 = 7 × 1,500 = ₹10,500. Ratio-based distribution is direct and linear in RAS questions; no efficiency multiplier unless explicitly stated.

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Last Updated

October 2026 | Verified for the RAS/RTS Combined Competitive Exam 2026 (Prelims scheduled 6 December 2026) | Content aligned with RPSC's RAS 2026 notification dated 27 May 2026