Time and Distance Questions for RRB NTPC

Core Relationship

Everything in this topic flows from one triangle: Speed, Distance, Time. Think of it like a pizza slice — Distance is the whole pizza, Speed and Time are the two things you cut it with. If you know any two, you can find the third. Unit conversion is the most common trap — always make sure speed, distance, and time are in matching units before applying the formula.

• Distance = Speed x Time (DST triangle — cover the one you want to find)
• Speed = Distance / Time
• Time = Distance / Speed
• To convert km/h to m/s: multiply by 5/18
• To convert m/s to km/h: multiply by 18/5
• 1 km/h = 5/18 m/s, so 18 km/h = 5 m/s (a handy benchmark)

Average Speed

Average speed is not the simple average of two speeds. This is the most common trap in the entire topic. When the same distance is covered at two different speeds, use the harmonic mean formula. Only use simple average when the same TIME is spent at two speeds (which is rare in questions).

• For equal distances at speed A and B: Average Speed = 2AB / (A + B)
• For equal time at speed A and B: Average Speed = (A + B) / 2
• If a person goes at 40 and returns at 60, average is NOT 50
• The answer is always less than the simple average when distances are equal
• Quick check: 2 x 40 x 60 / (40+60) = 4800/100 = 48 km/h

Relative Speed and Trains

When two objects move, their relative speed depends on direction. Opposite direction means they are closing in on each other fast, so add their speeds. Same direction means one is slowly catching up, so subtract. For trains, always remember to add the lengths of both objects involved — a train crossing a platform must cover its own length PLUS the platform length.

• Opposite direction: Relative Speed = S1 + S2
• Same direction: Relative Speed = S1 - S2 (faster minus slower)
• Train crossing a pole or person: Distance = Length of train only
• Train crossing a platform or bridge: Distance = Length of train + Length of platform
• Train crossing another train: Distance = Sum of both train lengths
• Time = Total Distance / Relative Speed

Boats and Streams

Boats and Streams is just relative speed in water clothing. The stream either helps or hurts the boat. Downstream means water helps, so speeds add. Upstream means fighting the current, so subtract. Think of it like cycling — with wind you go fast, against wind you slow down. If you know downstream and upstream speeds, you can find the boat speed and stream speed using simple averages.

• Downstream speed = Boat speed + Stream speed (u + v)
• Upstream speed = Boat speed - Stream speed (u - v)
• Boat speed in still water = (Downstream + Upstream) / 2
• Stream speed = (Downstream - Upstream) / 2
• Distance upstream = Distance downstream when time is the same (set up equation)

Meeting and Chasing Problems

When two people start from opposite ends and walk toward each other, time to meet = Total Distance / Sum of Speeds. When one person chases another, time to catch = Initial Gap / Difference of Speeds. Think of it as: approaching problems close the gap at (S1+S2) rate, chasing problems close the gap at (S1-S2) rate.

• Meeting (towards each other): Time = Total Distance / (S1 + S2)
• Chasing (same direction): Time = Gap / (S1 - S2)
• If they meet at point P, ratio of distances = ratio of speeds
• A and B start simultaneously: distance covered is proportional to speed

• Using simple average for average speed when equal distances are covered — always use 2AB/(A+B) in that case
• Forgetting to add the platform/bridge length to the train length — the full crossing distance is train + obstacle
• Not converting km/h to m/s when lengths are in metres and time is in seconds — mismatched units give wrong answers
• Confusing downstream speed with boat speed — downstream includes the stream boost, boat speed in still water is the average
• In chasing problems, dividing by the sum of speeds instead of the difference — use difference only when same direction

• DST Triangle: write D on top, S and T at bottom. Cover the letter you want — what remains is the operation to apply.
• 5-18 Rule: 5 goes to m/s (divide by 18), 18 goes to km/h (divide by 5). Think 5 is smaller like metres, 18 is bigger like kilometres.
• ADDS for water: Downstream ADDS, Upstream SUBTRACTS. DA = Downstream Add.
• Chasing and Meeting shortcut: Same direction = Subtract speeds. Opposite direction = Add speeds. SOSA — Same Subtract, Opposite Add.

• RRB NTPC typically gives 2-3 questions from this topic per paper. Train crossing and average speed are the most repeated question types — prioritize them.
• Unit conversion errors are the number one reason candidates lose marks here. Write down the unit at each step and convert at the very beginning.
• Boats and Streams questions in RRB NTPC are usually straightforward — finding boat speed or stream speed from given values. Rarely complex.
• For train problems, if the question says crosses a man or a pole, length to use is only the train length. Any stationary object with length means add both lengths.
• Average speed questions are set as traps — the two-speed scenario with equal distance appears almost every year. Do not fall for the simple average.