Quantitative Aptitude practice

Time and Distance Questions with Answers

Time and distance links speed, distance and time through one formula and extends to trains, boats and relative motion. Time and distance questions in SSC CGL, CHSL and MTS, RRB NTPC and Group D, and bank prelims ask for a speed, a train length, the time to cross a platform, or boat speeds in still water and stream. Tip: write the units beside every number and convert km/h to m/s (multiply by 5/18) before you start.

Formulas you need

Speed = Distance ÷ Time; Distance = Speed × Time; Time = Distance ÷ Speed
1 km/h = 5/18 m/s; 1 m/s = 18/5 km/h
Average speed = Total distance ÷ Total time
Equal distances at speeds a and b: average speed = 2ab ÷ (a + b)
Train crossing a pole: distance = length of train
Train crossing a platform: distance = length of train + length of platform
Two trains in opposite directions: relative speed = sum; same direction: difference
Boat: downstream speed = u + v; upstream speed = u − v (u = boat in still water, v = stream)
Boat speed in still water = ½ (downstream + upstream); stream speed = ½ (downstream − upstream)

Worked examples

Q1. A train runs at 72 km/h. How many metres does it cover in 15 seconds?

Convert: 72 × 5 ÷ 18 = 20 m/s
Distance = 20 × 15 = 300 m

Answer: 300 m

Q2. A 150 m long train crosses a 250 m long platform in 20 seconds. Find the speed of the train in km/h.

Distance covered = 150 + 250 = 400 m
Speed = 400 ÷ 20 = 20 m/s
In km/h: 20 × 18 ÷ 5 = 72

Answer: 72 km/h

Q3. A boat's speed in still water is 12 km/h and the stream flows at 3 km/h. It goes a certain distance downstream and returns to the starting point, taking 8 hours in all. Find the one-way distance.

Downstream speed = 12 + 3 = 15 km/h; upstream speed = 12 − 3 = 9 km/h
Let the distance be d: d ÷ 15 + d ÷ 9 = 8
d × (3 + 5) ÷ 45 = 8, so d × 8 ÷ 45 = 8
d = 45
Check: 45 ÷ 15 = 3 h and 45 ÷ 9 = 5 h, total 8 h

Answer: 45 km

Shortcuts that save time

Convert units once at the start. Most wrong answers in train questions come from mixing km/h and m/s, and the wrong option is always on the list.
For a round trip at two speeds, use 2ab ÷ (a + b) for the average speed. Averaging the two speeds directly gives a wrong answer that always appears as an option.
For trains crossing each other, add the lengths and add (or subtract) the speeds. Draw the direction of travel in one line to avoid choosing the wrong relative speed.

Where this appears

SSC CGL Tier-1	Quantitative Aptitude section
SSC CHSL Tier-1	Quantitative Aptitude section
SSC MTS	Numerical and Mathematical Ability section
RRB NTPC CBT-1	Mathematics section
Bank PO/Clerk Prelims	Quantitative Aptitude section