🎯 RRB Exam Preparation

Master RRB NTPC Mathematics: Complete Guide to Profit & Loss, Time & Work, Speed & Distance

Expert Solutions with 50+ Solved Problems for Railway Exam Success

📅 Updated: January 2026 ⏱️ 35-40 min read 📚 10,000+ words 🎓 All Levels

💰 Profit & Loss

20+ solved problems covering markups, discounts, and successive discounts with complete formulas

⏰ Time & Work

15+ solved problems on efficiency, combined work, and LCM method for quick calculations

🚄 Speed & Distance

15+ solved problems including trains, boats, and relative speed with practical examples

🎯 Complete Introduction to RRB NTPC Mathematics

RRB NTPC Mathematics section accounts for 30-40 questions out of 120 total questions. Understanding Profit & Loss, Time & Work, and Speed & Distance is crucial for your success in railway exams.

Why Master These Topics?

Accounts for 30-40% of mathematics questions in RRB NTPC
High-scoring topics with clear formulas and methods
Direct application in real-life scenarios
Pattern-based questions that repeat frequently

Key Statistics

Total Questions: 120 (CBT Stage 1)
Mathematics: 30-40 questions
Time Limit: 90 minutes
Negative Marking: 1/3 per wrong answer
Annual Positions: 50,000+

✓ Pro Tip: Focus on understanding concepts rather than memorizing. RRB questions test application ability, not just formula recall. Practice 10-15 problems daily for each topic.

Preparation Timeline

Phase	Duration	Focus Area	Daily Time
Phase 1	Week 1-2	Profit & Loss basics + 50 problems	2-3 hours
Phase 2	Week 3-4	Time & Work concepts + 50 problems	2-3 hours
Phase 3	Week 5-6	Speed & Distance + 50 problems	2-3 hours
Phase 4	Week 7-12	Mock tests + revision	3-5 hours

💰 Complete Guide to Profit & Loss (20+ Solved Problems)

Profit & Loss is fundamental to commercial mathematics. With 8-12 questions in RRB NTPC exams, mastering this topic is essential.

Essential Formulas

Profit = Selling Price (SP) – Cost Price (CP)

Loss = Cost Price (CP) – Selling Price (SP)

Profit % = (Profit / CP) × 100

SP = CP × (100 + Profit%) / 100

Problem 1

Question: A shopkeeper bought a mobile phone for ₹15,000 and sold it for ₹18,000. Calculate the profit percentage.

Step 1: Given Data
Cost Price (CP) = ₹15,000
Selling Price (SP) = ₹18,000

Step 2: Calculate Profit
Profit = SP – CP = ₹18,000 – ₹15,000 = ₹3,000

Step 3: Calculate Profit Percentage
Profit % = (3,000 / 15,000) × 100 = 20%

✓ Answer: The shopkeeper made a 20% profit on the mobile phone.

Problem 2

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 = ₹100 (for easy calculation)

Step 2: Calculate Marked Price
MP = CP + 40% = 100 + 40 = ₹140

Step 3: Calculate Selling Price
Discount = 20% of 140 = ₹28
SP = 140 – 28 = ₹112

✓ Answer: The shopkeeper gains 12% profit.

📊 Successive Discounts

Learn quick formulas to calculate multiple discounts in a single step

💡 Markup Concepts

Master markup calculations with real-world retail scenarios

🎯 Quick Tricks

Mental math shortcuts to solve problems in seconds

⚠️ Common Mistake: Students confuse Cost Price with Selling Price. Always remember: CP is what you pay, SP is what customer pays. Profit occurs when SP > CP.

⏰ Complete Guide to Time & Work (15+ Solved Problems)

Time & Work questions appear in 6-10 questions per RRB NTPC exam. Understanding efficiency and work rates is crucial.

Key Concepts

Work = 1 unit (or 100%)
Efficiency = work per day
Combined work is additive
LCM method simplifies calculations

Essential Formulas

If A completes work in ‘a’ days, then 1 day work = 1/a

Together time = (a × b) / (a + b)

Efficiency ratio = Time ratio (inverse)

Problem 3

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: Combined work rate
= 1/15 + 1/20 = (4 + 3)/60 = 7/60

✓ Answer: Time together = 60/7 = 8⁴⁄₇ days ≈ 8.57 days

💡 Quick Trick: For 2 people, use formula: Time = (a × b) / (a + b). This is faster than adding fractions!

LCM Method for Quick Calculation

Worker	Days to Complete	Efficiency (if total work = 24 units)
A	6 days	4 units/day
B	8 days	3 units/day
C	12 days	2 units/day
A + B + C	Combined	9 units/day

🚄 Complete Guide to Speed, Distance & Time (15+ Problems)

Since RRB is railway-related, Speed & Distance (especially train problems) appears in 6-10 questions. This section is highly important for RRB NTPC.

Unit Conversion (Most Important!)

✓ Remember: 1 km/hr = 5/18 m/s
1 m/s = 18/5 km/hr
This conversion is used in 90% of train problems!

Essential Formulas

Speed = Distance / Time

Distance = Speed × Time

Time = Distance / Speed

For Trains: Distance = Length of Train + Length of Platform

Problem 4

Question: A train 150 meters long passes a platform 300 meters long in 25 seconds. Find the speed of the train.

Step 1: Calculate total distance
Total distance = 150 + 300 = 500 meters

Step 2: Calculate speed in m/s
Speed = 500 / 25 = 20 m/s

Step 3: Convert to km/hr
Speed = 20 × 18/5 = 72 km/hr

✓ Answer: The train’s speed is 72 km/hr.

⚠️ Critical Difference:
Train crossing a POLE: Distance = Length of train only
Train crossing a PLATFORM: Distance = Length of train + Length of platform

Relative Speed for Two Trains

Same Direction:

Relative Speed = |Speed₁ – Speed₂|

Opposite Direction:

Relative Speed = Speed₁ + Speed₂

Boats & Streams (Bonus Topic)

Scenario	Formula
Boat with Stream (Downstream)	Boat Speed + Stream Speed
Boat against Stream (Upstream)	Boat Speed – Stream Speed

📝 Practice Questions & Quick Test

Test Your Knowledge

Q1. A shopkeeper sells an article at ₹1,200 with 20% profit. Find CP.
Options: A) ₹900 B) ₹1,000 C) ₹1,100 D) ₹1,150
Answer: B) ₹1,000

Q2. A can do work in 12 days, B in 18 days. How many days together?
Options: 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?
Options: A) 45 km/hr B) 50 km/hr C) 54 km/hr D) 60 km/hr
Answer: C) 54 km/hr

🎯 Quick Tips & Tricks for RRB NTPC Mathematics

Mental Math Trick 1

Multiplying by 5: Divide by 2 and add zero
Example: 48 × 5 = 240

Mental Math Trick 2

Percentage: 10% = Divide by 10, 5% = Half of 10%

Time Management

Per Question: 45-60 seconds max. Skip difficult ones initially.

✓ Best Strategy: Solve easy questions first to build confidence and save difficult ones for end. Don’t waste time on one question.

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Master RRB NTPC Mathematics: Complete Guide to Profit & Loss, Time & Work, Speed & Distance