Speed, Distance and Time Basics
Speed, Distance and Time Basics
Speed, distance and time is the backbone arithmetic topic in SBI Clerk Numerical Ability, feeding directly into trains, boats and even the time-and-work sums later in this chapter. The relationships are simple, but the exam rewards candidates who convert units instantly and pick the right formula without hesitation. Master the three-way link between the quantities here and every downstream topic becomes a short substitution rather than a fresh puzzle.
The Formula Triangle
All three quantities lock into one relationship: distance equals speed multiplied by time. Arrange them in a triangle with distance on top and speed and time below, and you can read off any formula by covering the quantity you want. Cover distance and you see speed times time; cover speed and you get distance over time; cover time and you get distance over speed. This single picture removes the guesswork about which quantity divides which, and it is the fastest way to stay error-free when a question mixes up the given values.
Distance = Speed × Time Speed = Distance / Time Time = Distance / Speed
Converting km/hr to m/s
SBI Clerk mixes units deliberately — a speed in kilometres per hour with a distance in metres — hoping you forget to convert. To change km/hr into m/s, multiply by 5/18; to go back from m/s to km/hr, multiply by 18/5. The logic is that one kilometre is 1000 metres and one hour is 3600 seconds, and 1000/3600 reduces to 5/18. Memorise the two multipliers as a reflex so that the moment a train speed appears in km/hr and a platform length in metres, you convert before you calculate rather than after a wrong answer.
✗ Leaving 72 km/hr as 72 while the length is in metres | ✓ Converting 72 × 5/18 = 20 m/s before using the length
Average Speed for Equal Distances
When a journey has two equal distances covered at different speeds, the average speed is not the plain average of the two speeds. Use the harmonic formula: average speed equals 2xy divided by (x + y), where x and y are the two speeds. A car going at 40 km/hr one way and 60 km/hr back averages 2×40×60 / 100 = 48 km/hr, not 50. The gap catches careless candidates every time, because more time is spent at the slower speed, which pulls the true average below the simple midpoint.
Average speed (equal distances) = 2xy / (x + y)
Solved Examples
Example 1: A cyclist covers 90 km in 3 hours, so speed = 90/3 = 30 km/hr. Example 2: A bus runs at 54 km/hr; in m/s that is 54 × 5/18 = 15 m/s, so in 12 seconds it covers 15 × 12 = 180 m. Example 3: A man walks 6 km at 4 km/hr and returns at 6 km/hr; average speed = 2×4×6 / 10 = 4.8 km/hr. Each answer is a single substitution once the units match.
| Constant quantity | Relationship | Exam use |
|---|---|---|
| Distance fixed | Speed and time inversely proportional | Same route, two trips |
| Time fixed | Distance and speed directly proportional | Same duration, compare distance |
| Speed fixed | Distance and time directly proportional | Same vehicle, longer trip |
The Proportionality Shortcut
Many questions never need the actual formula if you spot which quantity is constant. When distance is fixed, speed and time are inversely proportional, so doubling the speed halves the time; if the ratio of speeds is 4:5, the ratio of times is 5:4. When time is fixed, distance and speed move together in direct proportion. Reading a question through this proportional lens lets you answer 'if speed increases by 25 percent, by how much does time fall' in one line, without plugging numbers into the distance equation at all.
चाल = दूरी ÷ समय। km/hr को m/s में बदलने के लिए 5/18 से गुणा करें, और m/s को km/hr में बदलने के लिए 18/5 से। समान दूरी की औसत चाल = 2xy/(x+y) होती है, साधारण औसत नहीं।
Exam Pointer — SBI Clerk asks 1–2 direct speed-distance-time sums and uses this topic as the base for train and boat questions. The commonest trap is a unit mismatch, so convert km/hr to m/s with 5/18 first. Average-speed questions almost always test the 2xy/(x+y) formula, never the plain average — expect that catch.
60-Second Recap
- Distance = Speed × Time; use the triangle to pick the formula.
- km/hr → m/s: multiply by 5/18; reverse with 18/5.
- Average speed for equal distances = 2xy/(x+y), not (x+y)/2.
- Spot the constant quantity to use direct or inverse proportion.