Time Speed Distance Trains and Boats Questions for BIHAR POLICE CONSTABLE

Core Formula: Speed, Distance, Time

The foundation of all TSD problems. Speed is how fast something moves (km/h or m/s). Distance is how far it travels. Time is how long it takes. These three are linked by one simple relationship. Always check units before plugging numbers in — if distance is in metres and speed in km/h, convert first. Most mistakes happen here.

• Speed = Distance / Time; Distance = Speed × Time; Time = Distance / Speed
• Unit conversion: 1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h
• Always convert to same units before calculating
• In exams, watch for mixed units (km and metres in same question)

Train Crossing Problems

Train crossing is the most common TSD variant in Bihar Police exams. A train 'crosses' when it completely passes an object (pole, platform, another train). The key insight: when a train of length L crosses a pole, the train travels its own length L. When it crosses a platform of length P, it travels L + P. This is where most errors happen — students forget to add the platform length.

• Train crossing a pole: distance = length of train only
• Train crossing a platform/bridge: distance = length of train + length of platform
• Train crossing another train (head-on): distance = sum of both train lengths; use relative speed
• Train crossing another train (same direction): distance = sum of lengths; relative speed = difference of speeds

Relative Speed Concept

Relative speed is the speed of one object as seen from another. If two trains move towards each other, their relative speed is the sum of their speeds. If they move in the same direction, it is the difference. This concept applies to boats too. Think of it like this: if you are on a train moving at 60 km/h and another train passes you at 80 km/h in the same direction, you see it moving at 80 - 60 = 20 km/h relative to you.

• Head-on (opposite directions): Relative Speed = S1 + S2
• Same direction: Relative Speed = |S1 - S2| (absolute difference)
• Relative speed is always used when two moving objects interact
• In boat problems: upstream = boat speed - water speed; downstream = boat speed + water speed

Boat and Stream Problems

Boats move in water. The water has a current (speed). When a boat moves with the current (downstream), the current helps — add speeds. When against the current (upstream), the current opposes — subtract speeds. A common trap: students confuse which direction is upstream. Upstream = against the current (slower). Downstream = with the current (faster). In still water, the boat's speed is its own speed.

• Downstream speed = Boat speed + Stream speed
• Upstream speed = Boat speed - Stream speed
• Speed in still water = (Downstream + Upstream) / 2
• Stream speed = (Downstream - Upstream) / 2
• If boat speed < stream speed, boat cannot go upstream

Average Speed

Average speed is total distance divided by total time. A common mistake: students average the speeds instead of calculating total distance / total time. If you travel 100 km at 50 km/h and then 100 km at 100 km/h, your average speed is NOT 75 km/h. Calculate: total distance = 200 km, total time = 2 + 1 = 3 hours, average = 200/3 ≈ 66.67 km/h.

• Average Speed = Total Distance / Total Time (NOT average of speeds)
• If distances are equal but speeds differ, use harmonic mean formula
• If times are equal, use arithmetic mean of speeds

• Forgetting to convert units (km/h to m/s or vice versa) before calculation — always check units first
• In train crossing a platform, adding only the train length instead of train + platform length — this is the #1 error
• Confusing relative speed: using sum when it should be difference (or vice versa) for same-direction motion
• In boat problems, mixing up upstream and downstream or forgetting that upstream speed must be positive (boat speed > stream speed)
• Averaging speeds directly instead of using total distance / total time — this gives wrong answer almost always
• Misreading 'head-on' vs 'same direction' in two-train problems — changes the entire calculation

• TSD Triangle: Draw a triangle with D at top, S and T at bottom. Cover what you want; the remaining two show the formula. D = S × T, S = D/T, T = D/S.
• Train Crossing: 'Pole = Length only; Platform = Length + Platform' — think 'pole is a point, platform has size'
• Relative Speed: 'Head-on = Add (they rush towards each other); Same = Subtract (one chases the other)'
• Boat: 'Down = +, Up = -' — downstream adds stream speed, upstream subtracts it
• Average Speed: 'Total Distance over Total Time' — NOT average of speeds. Mnemonic: 'TDTT' (Total Distance Total Time)

• Bihar Police Constable typically has 1-2 easy TSD questions (basic speed/time or simple train crossing) and 1-2 moderate ones (relative speed, boats). Expect at least one train crossing question in every paper.
• Watch for unit conversion traps — questions often mix km and metres or km/h and m/s. Always convert to one unit before solving.
• Relative speed questions (two trains or boats) are moderately tricky but follow a formula. Identify 'head-on' vs 'same direction' immediately — this determines whether you add or subtract speeds.
• Boat problems are less common than train problems but when they appear, they test upstream/downstream logic. Practice the formulas for boat speed and stream speed from given data.
• Time management: TSD questions are solvable in 2-3 minutes if you know formulas. Don't spend more than 3 minutes per question; if stuck, skip and return. Accuracy matters more than speed here.