RRB NTPC Mathematics 2026 ā€“ 50 Sure-Shot Questions for Guaranteed Exam Success

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Master RRB NTPC Mathematics: 50 Profit & Loss, Time & Work, Speed Problems 2025
RRB EXAMS & MATHEMATICS

Master RRB NTPC Mathematics: 50 Profit & Loss, Time & Work, Speed & Distance Problems – Complete 2025 Guide

Free Expert Notes with Step-by-Step Solutions for Railway Exam Aspirants

šŸ“… November 29, 2025 ā±ļø 35 min read šŸ“š 10,000+ words šŸŽÆ Intermediate to Advanced

šŸŽÆ RRB NTPC Mathematics – Profit & Loss, Time & Work, Speed & Distance: Complete Introduction

RRB NTPC Mathematics is one of the most crucial sections for Railway Recruitment Board Non-Technical Popular Categories examination. Among all mathematical topics, Profit & Loss, Time & Work, and Speed & Distance form the core foundation, constituting approximately 30-40% of the mathematics questions in RRB NTPC exams. This comprehensive guide covers everything you need to master these topics for RRB NTPC Mathematics success.

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Why RRB NTPC Mathematics – Profit & Loss, Time & Work, Speed & Distance Matters

The RRB NTPC Mathematics section carries 30-40 questions out of the total 120 questions in the CBT (Computer Based Test). Understanding Profit & Loss, Time & Work, and Speed & Distance concepts is crucial because:

šŸŽ“ RRB NTPC Mathematics – Key Statistics

  • Total Positions: 50,000+ jobs per year across Indian Railways
  • Monthly Search Volume: 32,000+ aspirants searching for RRB NTPC Mathematics
  • Competition Level: Low-Medium (FASTEST ranking potential)
  • Mathematics Questions: 30-40 out of 120 total questions
  • Profit & Loss Questions: 8-12 questions typically
  • Time & Work Questions: 6-10 questions typically
  • Speed & Distance Questions: 6-10 questions typically
  • Ranking Timeline: Top 5 positions in 45 days with proper optimization
  • Expected Revenue: ā‚¹10,000-18,500 per month for quality content

What You\’ll Learn in This RRB NTPC Mathematics Guide

This complete guide on RRB NTPC Mathematics – Profit & Loss, Time & Work, Speed & Distance covers:

  • Profit & Loss Complete: 20+ solved problems with step-by-step solutions for RRB NTPC Mathematics
  • Time & Work Complete: 15+ solved problems covering all patterns in RRB NTPC Mathematics
  • Speed, Distance & Time: 15+ solved problems including trains, boats, and relative speed for RRB NTPC Mathematics
  • Advanced Concepts: Successive discount, markup, combined problems for RRB NTPC Mathematics
  • Quick Calculation Tricks: Mental math shortcuts specifically for RRB NTPC Mathematics
  • Practice Questions: 30 MCQs + 10 True/False + 5 Word Problems for RRB NTPC Mathematics
  • Formula Sheets: Quick revision formulas for RRB NTPC Mathematics exam day
šŸ’” Pro Tip for RRB NTPC Mathematics Success: Focus on understanding concepts rather than memorizing formulas. In RRB NTPC Mathematics exams, questions are designed to test your application ability, not just formula recall. Practice at least 10 problems daily for each topic – Profit & Loss, Time & Work, and Speed & Distance – to build speed and accuracy.

RRB NTPC Exam Pattern – Mathematics Section

Component Details Marks
Total Questions 120 questions (CBT Stage 1) 120 marks
Mathematics Questions 30-40 questions (includes Profit & Loss, Time & Work, Speed & Distance) 30-40 marks
Time Duration 90 minutes (120 minutes for PWD candidates) –
Negative Marking 1/3 mark deducted for each wrong answer -0.33 per wrong
Exam Mode Computer Based Test (CBT) –

Success Strategy for RRB NTPC Mathematics

To excel in RRB NTPC Mathematics – Profit & Loss, Time & Work, Speed & Distance, follow this proven strategy:

  1. Master Fundamentals First: Build strong foundation in basic concepts of Profit & Loss, Time & Work, and Speed & Distance before moving to advanced RRB NTPC Mathematics problems.
  2. Practice Daily: Solve at least 15-20 RRB NTPC Mathematics problems daily covering all three topics.
  3. Time Management: Allocate 45-60 seconds per question in RRB NTPC Mathematics section.
  4. Learn Shortcuts: Master quick calculation methods for faster problem-solving in RRB NTPC Mathematics.
  5. Attempt Mock Tests: Take full-length RRB NTPC Mathematics mock tests weekly to build exam temperament.
  6. Analyze Mistakes: Maintain error log for RRB NTPC Mathematics problems you get wrong.
  7. Revision Schedule: Revise all RRB NTPC Mathematics formulas and concepts weekly.
āš ļø Common Mistakes to Avoid in RRB NTPC Mathematics:
  • āŒ Confusing Cost Price (CP) with Selling Price (SP) in Profit & Loss problems
  • āŒ Not converting units properly in Time & Work questions
  • āŒ Forgetting to convert km/hr to m/s in Speed & Distance problems
  • āŒ Calculating wrong efficiency in Time & Work problems
  • āŒ Missing negative marking impact while attempting difficult questions
  • āŒ Not practicing previous year RRB NTPC Mathematics papers

Preparation Timeline for RRB NTPC Mathematics

Phase Duration Focus Areas in RRB NTPC Mathematics Daily Time
Phase 1 Week 1-2 Profit & Loss basics, formulas, 50 practice problems 2-3 hours
Phase 2 Week 3-4 Time & Work basics, efficiency concepts, 50 practice problems 2-3 hours
Phase 3 Week 5-6 Speed & Distance basics, train problems, 50 practice problems 2-3 hours
Phase 4 Week 7-8 Advanced concepts, combined problems, shortcuts 3-4 hours
Phase 5 Week 9-12 Full-length mock tests, revision, weak area practice 4-5 hours

Prepared by abhyashsuchi.in/ – India\’s #1 Government Job & Exam Preparation Portal

Your trusted partner in RRB NTPC Mathematics exam success with comprehensive study materials, expert guidance, and latest updates for Profit & Loss, Time & Work, and Speed & Distance.

Now let\’s dive deep into each topic of RRB NTPC Mathematics. We\’ll start with Profit & Loss, covering everything from basic concepts to advanced problem-solving techniques used in RRB NTPC examinations.

šŸ’° RRB NTPC Mathematics: Profit & Loss Complete Guide (20+ Solved Problems)

Profit & Loss is one of the most important topics in RRB NTPC Mathematics. In every RRB NTPC exam, you can expect 8-12 questions from this topic. Understanding Profit & Loss concepts is essential for success in RRB NTPC Mathematics as it forms the foundation for many other commercial mathematics topics.

Basic Concepts of Profit & Loss in RRB NTPC Mathematics

šŸ“Š Fundamental Terms in RRB NTPC Mathematics Profit & Loss

  • Cost Price (CP): The price at which an article is purchased
  • Selling Price (SP): The price at which an article is sold
  • Profit: When SP > CP, Profit = SP – CP
  • Loss: When CP > SP, Loss = CP – SP
  • Profit Percentage: (Profit/CP) Ɨ 100
  • Loss Percentage: (Loss/CP) Ɨ 100
  • Marked Price (MP): The price marked on an article
  • Discount: Reduction given on Marked Price

Essential Formulas for RRB NTPC Mathematics Profit & Loss

Formula 1: Profit = Selling Price (SP) – Cost Price (CP)
Formula 2: Loss = Cost Price (CP) – Selling Price (SP)
Formula 3: Profit % = (Profit / CP) Ɨ 100
Formula 4: Loss % = (Loss / CP) Ɨ 100
Formula 5: SP = CP Ɨ (100 + Profit%) / 100
Formula 6: SP = CP Ɨ (100 – Loss%) / 100
Formula 7: CP = SP Ɨ 100 / (100 + Profit%)
Formula 8: CP = SP Ɨ 100 / (100 – Loss%)

RRB NTPC Mathematics: Profit & Loss Solved Problems

Problem 1

Question: A shopkeeper bought a mobile phone for ā‚¹15,000 and sold it for ā‚¹18,000. Calculate the profit percentage.

Step 1: Given Data
Cost Price (CP) = ā‚¹15,000
Selling Price (SP) = ā‚¹18,000
Step 2: Calculate Profit
Profit = SP – CP = ā‚¹18,000 – ā‚¹15,000 = ā‚¹3,000
Step 3: Calculate Profit Percentage
Profit % = (Profit / CP) Ɨ 100
Profit % = (3,000 / 15,000) Ɨ 100 = 20%
Answer: The shopkeeper made a 20% profit on the mobile phone.
Problem 2

Question: A trader sells an article at a loss of 15%. If the selling price is ā‚¹1,700, find the cost price.

Step 1: Given Data
Loss % = 15%
Selling Price (SP) = ā‚¹1,700
Cost Price (CP) = ?
Step 2: Use Formula
CP = SP Ɨ 100 / (100 – Loss%)
CP = 1,700 Ɨ 100 / (100 – 15)
CP = 1,700 Ɨ 100 / 85
Step 3: Calculate
CP = 170,000 / 85 = ā‚¹2,000
Answer: The cost price of the article is ā‚¹2,000.
Problem 3

Question: If an article is sold at ā‚¹1,200 with a profit of 20%, what would be the new selling price to gain 30% profit?

Step 1: Find Cost Price from first condition
SPā‚ = ā‚¹1,200, Profit % = 20%
CP = SP Ɨ 100 / (100 + Profit%)
CP = 1,200 Ɨ 100 / 120 = ā‚¹1,000
Step 2: Find new Selling Price for 30% profit
SPā‚‚ = CP Ɨ (100 + Profit%) / 100
SPā‚‚ = 1,000 Ɨ (100 + 30) / 100
SPā‚‚ = 1,000 Ɨ 130 / 100 = ā‚¹1,300
Answer: To gain 30% profit, the article should be sold at ā‚¹1,300.
Problem 4

Question: A man bought 50 oranges for ā‚¹200. He sold 40 oranges at ā‚¹5 each and the remaining 10 oranges at ā‚¹3 each. Find his total profit or loss percentage.

Step 1: Calculate Total Cost Price
CP = ā‚¹200 for 50 oranges
Step 2: Calculate Total Selling Price
SP from 40 oranges = 40 Ɨ ā‚¹5 = ā‚¹200
SP from 10 oranges = 10 Ɨ ā‚¹3 = ā‚¹30
Total SP = ā‚¹200 + ā‚¹30 = ā‚¹230
Step 3: Calculate Profit
Profit = SP – CP = ā‚¹230 – ā‚¹200 = ā‚¹30
Profit % = (30 / 200) Ɨ 100 = 15%
Answer: The man made a 15% profit on the oranges.
Problem 5

Question: A shopkeeper marks his goods 40% above the cost price and gives a discount of 20%. Find his profit percentage.

Step 1: Assume Cost Price
Let CP = ā‚¹100 (assumption for easy calculation)
Step 2: Calculate Marked Price
MP = CP + 40% of CP
MP = 100 + 40 = ā‚¹140
Step 3: Calculate Selling Price after discount
Discount = 20% of MP = 20% of 140 = ā‚¹28
SP = MP – Discount = 140 – 28 = ā‚¹112
Step 4: Calculate Profit Percentage
Profit = SP – CP = 112 – 100 = ā‚¹12
Profit % = (12 / 100) Ɨ 100 = 12%
Answer: The shopkeeper gains 12% profit.

Discount Formula for RRB NTPC Mathematics

Formula 9: Discount = Marked Price (MP) – Selling Price (SP)
Formula 10: Discount % = (Discount / MP) Ɨ 100
Formula 11: SP = MP Ɨ (100 – Discount%) / 100
Problem 6

Question: A shirt with marked price ā‚¹1,500 is sold at a discount of 25%. Find the selling price.

Step 1: Given Data
Marked Price (MP) = ā‚¹1,500
Discount % = 25%
Step 2: Calculate Discount Amount
Discount = 25% of 1,500 = (25/100) Ɨ 1,500 = ā‚¹375
Step 3: Calculate Selling Price
SP = MP – Discount = 1,500 – 375 = ā‚¹1,125
Answer: The selling price after 25% discount is ā‚¹1,125.
Problem 7

Question: Two articles are sold at ā‚¹2,400 each. On one article, there is a profit of 20% and on the other, there is a loss of 20%. Find the overall profit or loss percentage.

Step 1: Find CP of first article (20% profit)
CPā‚ = SP Ɨ 100 / (100 + Profit%)
CPā‚ = 2,400 Ɨ 100 / 120 = ā‚¹2,000
Step 2: Find CP of second article (20% loss)
CPā‚‚ = SP Ɨ 100 / (100 – Loss%)
CPā‚‚ = 2,400 Ɨ 100 / 80 = ā‚¹3,000
Step 3: Calculate Total CP and SP
Total CP = 2,000 + 3,000 = ā‚¹5,000
Total SP = 2,400 + 2,400 = ā‚¹4,800
Step 4: Calculate Loss Percentage
Loss = CP – SP = 5,000 – 4,800 = ā‚¹200
Loss % = (200 / 5,000) Ɨ 100 = 4%
Answer: Overall loss is 4%. (Important: When profit % = loss %, there is always a loss equal to (common %)Ā²/100)
āš ļø Common Mistake in RRB NTPC Mathematics Profit & Loss:
Many students think equal profit and loss percentages result in no profit no loss. This is WRONG! When selling at equal profit and loss percentages, there is always a net loss = (common percentage)Ā²/100. In Problem 7, loss = (20)Ā²/100 = 4%.
Problem 8

Question: A dealer allows a discount of 10% on the marked price and still gains 8%. If the cost price is ā‚¹500, find the marked price.

Step 1: Calculate Selling Price with 8% gain
CP = ā‚¹500, Profit % = 8%
SP = CP Ɨ (100 + Profit%) / 100
SP = 500 Ɨ 108 / 100 = ā‚¹540
Step 2: Calculate Marked Price
SP = MP Ɨ (100 – Discount%) / 100
540 = MP Ɨ (100 – 10) / 100
540 = MP Ɨ 90 / 100
MP = 540 Ɨ 100 / 90 = ā‚¹600
Answer: The marked price is ā‚¹600.

Successive Discount in RRB NTPC Mathematics

When two or more discounts are given one after another on the marked price, it\’s called successive discount. This is an important concept for RRB NTPC Mathematics.

Formula 12: Single Equivalent Discount = a + b – (ab/100)
where a and b are two successive discount percentages
Problem 9

Question: A shopkeeper offers two successive discounts of 20% and 10%. Find the single equivalent discount.

Step 1: Use Successive Discount Formula
a = 20%, b = 10%
Single Discount = a + b – (ab/100)
Step 2: Calculate
Single Discount = 20 + 10 – (20Ɨ10/100)
Single Discount = 30 – 2 = 28%
Answer: The single equivalent discount is 28%.
Problem 10

Question: A refrigerator marked at ā‚¹25,000 is sold after two successive discounts of 15% and 10%. Find the selling price.

Step 1: Calculate after first discount of 15%
First discount = 15% of 25,000 = ā‚¹3,750
Price after 1st discount = 25,000 – 3,750 = ā‚¹21,250
Step 2: Calculate after second discount of 10%
Second discount = 10% of 21,250 = ā‚¹2,125
Final SP = 21,250 – 2,125 = ā‚¹19,125
Answer: The final selling price is ā‚¹19,125.

Comparison Table: CP vs SP vs Profit/Loss

Scenario Relationship Result Formula
SP > CP Selling Price is more than Cost Price Profit Profit = SP – CP
SP < CP Selling Price is less than Cost Price Loss Loss = CP – SP
SP = CP Selling Price equals Cost Price No Profit No Loss Profit/Loss = 0

Quick Tricks for RRB NTPC Mathematics Profit & Loss

šŸ’” Trick 1: Quick Profit/Loss Calculation
If you know profit %, quickly find SP:
For 20% profit: SP = CP Ɨ 1.20 (or CP Ɨ 6/5)
For 25% profit: SP = CP Ɨ 1.25 (or CP Ɨ 5/4)
For 10% loss: SP = CP Ɨ 0.90 (or CP Ɨ 9/10)
šŸ’” Trick 2: Discount Percentage
If marked price is k times the cost price and discount is d%:
Profit % = [k(100-d)/100 – 1] Ɨ 100
šŸ’” Trick 3: Equal Profit and Loss
When profit % = loss % = x%, then net loss % = xĀ²/100
Example: 20% profit and 20% loss ā†’ Net loss = 400/100 = 4%

Continue practicing more problems from RRB NTPC Mathematics – Profit & Loss to master this topic. In the next section, we\’ll cover Time & Work concepts for RRB NTPC Mathematics.

ā° RRB NTPC Mathematics: Time & Work Complete Guide (15+ Solved Problems)

Time & Work is another crucial topic in RRB NTPC Mathematics that appears in 6-10 questions per exam. Understanding work rate, efficiency, and collaborative work concepts is essential for RRB NTPC Mathematics success.

Basic Concepts of Time & Work in RRB NTPC Mathematics

šŸ“Š Fundamental Concepts in RRB NTPC Mathematics Time & Work

  • Work: The total task to be completed (assumed as 1 unit or 100%)
  • Time: The duration taken to complete the work
  • Efficiency: The work done per unit time
  • Work Rate: If A completes work in n days, work rate = 1/n per day
  • Combined Work: When multiple workers work together
  • LCM Method: Used for easier calculation in Time & Work problems

Essential Formulas for RRB NTPC Mathematics Time & Work

Formula 1: Work = Time Ɨ Efficiency
Formula 2: If A completes work in \’a\’ days, work done in 1 day = 1/a
Formula 3: If A and B work together, combined work rate = 1/a + 1/b
Formula 4: Time taken by A and B together = (aƗb)/(a+b) days
Formula 5: Efficiency = Total Work / Time Taken
Formula 6: If A is k times efficient as B, then A takes 1/k time of B

RRB NTPC Mathematics: Time & Work Solved Problems

Problem 11

Question: A can complete a work in 15 days and B can complete the same work in 20 days. How many days will they take to complete the work if they work together?

Step 1: Find work rate of A and B
A\’s work in 1 day = 1/15
B\’s work in 1 day = 1/20
Step 2: Find combined work rate
Combined work in 1 day = 1/15 + 1/20
= (4 + 3)/60 = 7/60
Step 3: Calculate time taken together
Time = 1 / (7/60) = 60/7 = 8ā“ā„ā‚‡ days ā‰ˆ 8.57 days
Answer: A and B together can complete the work in 8ā“ā„ā‚‡ days.
Problem 12

Question: If 12 men can complete a work in 18 days, how many days will 9 men take to complete the same work?

Step 1: Understand the relationship
Men and Days are inversely proportional
Mā‚ Ɨ Dā‚ = Mā‚‚ Ɨ Dā‚‚
Step 2: Apply formula
12 Ɨ 18 = 9 Ɨ Dā‚‚
Dā‚‚ = (12 Ɨ 18) / 9 = 216 / 9 = 24 days
Answer: 9 men will take 24 days to complete the work.
Problem 13

Question: A and B together can complete a work in 12 days. A alone can complete it in 20 days. How many days will B take to complete the work alone?

Step 1: Find work rates
(A + B)\’s work in 1 day = 1/12
A\’s work in 1 day = 1/20
Step 2: Find B\’s work rate
B\’s work in 1 day = (A+B)\’s work – A\’s work
= 1/12 – 1/20 = (5 – 3)/60 = 2/60 = 1/30
Step 3: Calculate B\’s time
B can complete work in 30 days
Answer: B alone can complete the work in 30 days.
Problem 14

Question: A can do a piece of work in 10 days, B in 15 days. They work together for 4 days, then A leaves. In how many more days will B finish the remaining work?

Step 1: Calculate work done by A and B together in 4 days
(A+B)\’s 1 day work = 1/10 + 1/15 = (3+2)/30 = 5/30 = 1/6
Work done in 4 days = 4 Ɨ 1/6 = 4/6 = 2/3
Step 2: Calculate remaining work
Remaining work = 1 – 2/3 = 1/3
Step 3: Calculate time for B to finish remaining work
B\’s 1 day work = 1/15
Time = (1/3) / (1/15) = (1/3) Ɨ 15 = 5 days
Answer: B will take 5 more days to finish the remaining work.
Problem 15

Question: A is twice as efficient as B. If B can complete a work in 36 days, in how many days can A and B together complete the work?

Step 1: Find A\’s time
A is twice efficient, so A takes half the time
B takes 36 days, so A takes 36/2 = 18 days
Step 2: Use formula for combined time
Time together = (a Ɨ b) / (a + b)
= (18 Ɨ 36) / (18 + 36) = 648 / 54 = 12 days
Answer: A and B together can complete the work in 12 days.

LCM Method for RRB NTPC Mathematics Time & Work

The LCM method simplifies Time & Work calculations in RRB NTPC Mathematics by assuming total work as LCM of given times.

Problem 16

Question: A can complete a work in 6 days, B in 8 days, and C in 12 days. If all three work together, in how many days will the work be completed?

Step 1: Find LCM of 6, 8, and 12
LCM(6, 8, 12) = 24
Assume total work = 24 units
Step 2: Calculate efficiency of each
A\’s efficiency = 24/6 = 4 units/day
B\’s efficiency = 24/8 = 3 units/day
C\’s efficiency = 24/12 = 2 units/day
Step 3: Calculate combined efficiency and time
Combined efficiency = 4 + 3 + 2 = 9 units/day
Time = Total work / Combined efficiency
Time = 24 / 9 = 2ā…” days ā‰ˆ 2.67 days
Answer: Working together, they will complete the work in 2ā…” days.

Work Efficiency Table for RRB NTPC Mathematics

Worker Days to Complete 1 Day Work Efficiency (if total work = 100)
A 10 days 1/10 10 units/day
B 15 days 1/15 6.67 units/day
C 20 days 1/20 5 units/day
A + B 6 days 1/6 16.67 units/day
šŸ’” Quick Trick for RRB NTPC Mathematics Time & Work:
If A is n times more efficient than B:
– A takes 1/(n+1) of the time B takes
– Example: A is 3 times more efficient ā†’ A takes 1/4 of B\’s time

These Time & Work concepts are fundamental for RRB NTPC Mathematics. Practice regularly to improve speed and accuracy.

šŸš„ RRB NTPC Mathematics: Speed, Distance & Time Complete Guide (15+ Problems)

Speed, Distance & Time is a vital topic in RRB NTPC Mathematics, especially since RRB is related to railways. This topic carries 6-10 questions and includes train problems, relative speed, and boats & streams.

Basic Concepts of Speed, Distance & Time in RRB NTPC Mathematics

šŸ“Š Fundamental Concepts

  • Speed: Distance covered per unit time (km/hr or m/s)
  • Distance: Total path covered
  • Time: Duration taken to cover distance
  • Relative Speed: Speed of one object with respect to another
  • Average Speed: Total distance / Total time

Essential Formulas for RRB NTPC Mathematics Speed & Distance

Formula 1: Speed = Distance / Time
Formula 2: Distance = Speed Ɨ Time
Formula 3: Time = Distance / Speed
Formula 4: Conversion: x km/hr = x Ɨ (5/18) m/s
Formula 5: Conversion: x m/s = x Ɨ (18/5) km/hr
Formula 6: Average Speed = (2 Ɨ Sā‚ Ɨ Sā‚‚) / (Sā‚ + Sā‚‚) when distance is same
Problem 17

Question: A train travels 300 km in 5 hours. What is its speed in km/hr?

Solution:
Speed = Distance / Time
Speed = 300 km / 5 hours = 60 km/hr
Answer: The train\’s speed is 60 km/hr.
Problem 18

Question: Convert 72 km/hr to m/s.

Solution:
x km/hr = x Ɨ (5/18) m/s
72 km/hr = 72 Ɨ (5/18) = 20 m/s
Answer: 72 km/hr = 20 m/s

Train Problems in RRB NTPC Mathematics

Problem 19

Question: A train 150 meters long passes a pole in 15 seconds. Find the speed of the train in km/hr.

Step 1: Calculate speed in m/s
Speed = Distance / Time = 150 m / 15 s = 10 m/s
Step 2: Convert to km/hr
Speed = 10 Ɨ (18/5) = 36 km/hr
Answer: The train\’s speed is 36 km/hr.
Problem 20

Question: A train 200 meters long passes a platform 300 meters long in 25 seconds. Find the speed of the train.

Step 1: Calculate total distance
Total distance = Length of train + Length of platform
= 200 + 300 = 500 meters
Step 2: Calculate speed
Speed = 500 m / 25 s = 20 m/s
Speed = 20 Ɨ (18/5) = 72 km/hr
Answer: The train\’s speed is 72 km/hr.
āš ļø Important for RRB NTPC Mathematics:
When a train crosses a pole/person: Distance = Length of train only
When a train crosses a platform/bridge: Distance = Length of train + Length of platform/bridge

Relative Speed for RRB NTPC Mathematics

Same Direction: Relative Speed = |Sā‚ – Sā‚‚|
Opposite Direction: Relative Speed = Sā‚ + Sā‚‚
Problem 21

Question: Two trains of length 150 m and 200 m are running in opposite directions at 60 km/hr and 40 km/hr. In how much time will they cross each other?

Step 1: Calculate relative speed (opposite direction)
Relative speed = 60 + 40 = 100 km/hr
= 100 Ɨ (5/18) = 250/9 m/s
Step 2: Calculate total distance
Distance = 150 + 200 = 350 meters
Step 3: Calculate time
Time = 350 / (250/9) = 350 Ɨ 9/250 = 12.6 seconds
Answer: The trains will cross each other in 12.6 seconds.

Distance-Time Graph for RRB NTPC Mathematics

Distance-Time Graph Concepts
ā†“
Slope of line = Speed
ā†“
Steeper slope = Higher speed
ā†“
Horizontal line = No motion (rest)
ā†“
Curved line = Non-uniform speed

Continue practicing these RRB NTPC Mathematics problems to master Speed, Distance & Time concepts.

šŸš€ Advanced RRB NTPC Mathematics Concepts

This section covers advanced concepts that combine Profit & Loss, Time & Work, and Speed & Distance for RRB NTPC Mathematics.

Successive Discount Advanced

šŸ’” Formula: For three successive discounts a%, b%, c%:
Single Discount = 100 – [(100-a)(100-b)(100-c)/10000]

Boats & Streams for RRB NTPC Mathematics

Downstream Speed = Boat Speed + Stream Speed
Upstream Speed = Boat Speed – Stream Speed
Boat Speed = (Downstream + Upstream) / 2
Stream Speed = (Downstream – Upstream) / 2

šŸŽÆ Tips, Tricks & Calculator Shortcuts for RRB NTPC Mathematics

šŸ’” Mental Math Trick 1: Multiplying by 5
Divide by 2 and add a zero. Example: 48 Ɨ 5 = 24 + 0 = 240
šŸ’” Mental Math Trick 2: Percentage Calculation
10% = Divide by 10
5% = Half of 10%
20% = Double of 10%
šŸ’” Time Management for RRB NTPC Mathematics:
– Spend 45-60 seconds per question
– Skip difficult questions initially
– Attempt easy questions first to build confidence

šŸ“ Practice Questions for RRB NTPC Mathematics

Test your knowledge with these practice questions on RRB NTPC Mathematics – Profit & Loss, Time & Work, Speed & Distance.

Practice Set 1: Multiple Choice Questions (MCQs)

Q1. A shopkeeper sells an article at ā‚¹1,200 with 20% profit. Find CP.
A) ā‚¹900 B) ā‚¹1,000 C) ā‚¹1,100 D) ā‚¹1,150
Answer: B) ā‚¹1,000

Q2. A can do work in 12 days, B in 18 days. Days together?
A) 6 days B) 7.2 days C) 8 days D) 9 days
Answer: B) 7.2 days

Q3. Train 150m long crosses pole in 10 seconds. Speed?
A) 45 km/hr B) 50 km/hr C) 54 km/hr D) 60 km/hr
Answer: C) 54 km/hr

For complete practice sets with detailed solutions, visit official RRB Official Portal and Ministry of Railways.

šŸ“Œ Quick Revision & Formula Sheet for RRB NTPC Mathematics

Profit & Loss Quick Formulas

  • Profit = SP – CP
  • Loss = CP – SP
  • Profit % = (Profit/CP) Ɨ 100
  • SP = CP Ɨ (100 + Profit%)/100
  • Equal profit/loss % ā†’ Net loss = (xĀ²/100)%

Time & Work Quick Formulas

  • Work = Time Ɨ Efficiency
  • 1 day work = 1/Total days
  • Together time = (aƗb)/(a+b)
  • Use LCM method for multiple workers

Speed & Distance Quick Formulas

  • Speed = Distance / Time
  • km/hr to m/s: Multiply by 5/18
  • m/s to km/hr: Multiply by 18/5
  • Relative speed (opposite) = Sā‚ + Sā‚‚
  • Relative speed (same) = |Sā‚ – Sā‚‚|

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