SSC CGL Reasoning · Arithmetic Reasoning

Speed, Time and Work

Speed is distance over time in matching units, a stream adds to or takes from a boat's speed, and a job's total work (workers times time) stays the same however it is shared.

All Arithmetic Reasoning notes

Why this matters

Eleven questions in the bank, all EASY and all from the 2025 shifts. Five are about speed, trains or an average speed, two about a boat in a stream, and four about machines, taps, pipes or cats sharing one job.

Concept 1 of 3: Speed, trains and average speed

Every question here is speed equals distance over time, once the units match. A train is the one twist: to pass something it must cover its own length, plus the length of whatever it passes.

Definition

Speed $=$ distance $\div$ time. Put distance and time in matching units first: 45 minutes is $\frac{3}{4}$ hour.
Units: km/h to m/s, multiply by $\frac{5}{18}$ ; m/s to km/h, multiply by $\frac{18}{5}$ .
A train passing a pole, a man or a point covers its own length. Passing a platform or a bridge, it covers its length plus the platform's.
Average speed $=$ total distance $\div$ total time. Never the average of the two speeds unless the two times are equal.
Shortcut for two equal distances at speeds a and b: $\frac{2ab}{a + b}$ . It is only for equal distances; for equal times the average speed is $\frac{a + b}{2}$ .

Speed, units and average speed

v = \frac{d}{t} \qquad 1\ \text{km/h} = \frac{5}{18}\ \text{m/s} \qquad \bar{v} = \frac{2ab}{a + b}

d, tdistance and time
a, bthe speeds over two equal distances

Worked example

A train 240 m long runs at 54 km/h. How long does it take to cross a platform 210 m long?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 21 Sep 2025, Shift 3 · Q23Easy

Example 1 · Arithmetic Reasoning · Speed, Time and Work

A train 120 meters long takes 6 seconds to cross a man. What is the speed of the train in km/h?

Using the equal-distance shortcut for equal times

\frac{2ab}{a + b}

is for two equal distances. If the two parts take equal times, the average speed is the simple average

\frac{a + b}{2}

Forgetting the platform's length

A train crossing a platform has crossed it only when its last coach leaves the far end, so the distance is the train's length plus the platform's.

Drill 4 more on speed, trains and average speed

Concept 2 of 3: Boats and streams

Going with the stream, the water carries the boat along; going against it, the water holds it back. The two speeds sit an equal distance above and below the boat's own speed.

Definition

Downstream speed $=$ boat $+$ stream. Upstream speed $=$ boat $-$ stream.
So the boat's speed in still water is half the sum of the two, and the stream's speed is half their difference.
First turn each trip into a speed (distance $\div$ time), then use the half-sum and half-difference.

Boat and stream from the two speeds

b = \frac{d + u}{2} \qquad s = \frac{d - u}{2}

dthe downstream speed
uthe upstream speed
b, sthe speeds of the boat in still water and of the stream

Worked example

A boat goes 75 km downstream in 5 hours and 28 km upstream in 4 hours. Find its speed in still water and the speed of the stream.

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 18 Sep 2025, Shift 1 · Q21Easy

Example 2 · Arithmetic Reasoning · Speed, Time and Work

A boat travels 60 kilometers upstream in 3 hours and covers the same distance of 60 kilometers downstream in 2 hours. What is the speed of the boat in still water?

Swapping the boat and the stream

Half the sum of the two speeds is the boat's speed in still water; half the difference is the stream's. The stream is almost always the smaller number.

Averaging distances instead of speeds

When the two trips have different distances, first divide each distance by its time. The half-sum rule works on speeds only.

Drill 1 more on boats and streams

Concept 3 of 3: Work, taps and pipes

A job needs a fixed amount of work, counted as workers times time (machine-days, tap-minutes). More workers share it and finish sooner. A pipe that empties the tank works against the ones that fill it.

Definition

Total work $=$ workers $\times$ time. For the same job at the same rate, $W_1 T_1 = W_2 T_2$ : double the workers, half the time.
A bigger or smaller job: first find what one worker does in one unit of time, then scale. This is how "5 cats catch 5 mice in 5 minutes" works: one cat catches one mouse in 5 minutes.
Pipes (fast route): call the tank the LCM of the times, in units. Each pipe fills (or empties) a whole number of units an hour. Add the fillers, subtract the emptiers, divide the tank by the net rate.
The workers-times-time rule assumes everyone works at the same rate. If the rates differ, use units per hour for each.

Same job, and pipes working together

W_1 T_1 = W_2 T_2 \qquad \frac{1}{T} = \frac{1}{a} - \frac{1}{b}

W, Tnumber of workers and time taken
atime for the filling pipe alone
btime for the emptying pipe alone

Worked example

A pipe fills a tank in 9 hours and a drain empties it in 12 hours. If both are open, how long does the empty tank take to fill?

Practice this conceptself-check · 4 quick reps

The same idea in a real exam question:

SSC CGL · 2025 · Tier I, 19 Sep 2025, Shift 1 · Q21Easy

Example 3 · Arithmetic Reasoning · Speed, Time and Work

If 4 taps can fill a tank in 15 minutes, how many taps are needed to fill it in 6 minutes?

Treating workers and time as direct

More workers means fewer days, not more. If 4 machines take 12 days, 8 machines take 6 days.

Adding the emptying pipe

An outlet takes water away, so its rate is subtracted from the inlet's. Adding it gives a time that is far too short.

Drill 3 more on work, taps and pipes

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (3)

Speed, trains and average speed
Speed, units and average speed
$v = \frac{d}{t} \qquad 1\ \text{km/h} = \frac{5}{18}\ \text{m/s} \qquad \bar{v} = \frac{2ab}{a + b}$
Boats and streams
Boat and stream from the two speeds
$b = \frac{d + u}{2} \qquad s = \frac{d - u}{2}$
Work, taps and pipes
Same job, and pipes working together
$W_1 T_1 = W_2 T_2 \qquad \frac{1}{T} = \frac{1}{a} - \frac{1}{b}$

Watch out for (6)

Using the equal-distance shortcut for equal times
→ Speed, trains and average speed
Forgetting the platform's length
→ Speed, trains and average speed
Swapping the boat and the stream
→ Boats and streams
Averaging distances instead of speeds
→ Boats and streams
Treating workers and time as direct
→ Work, taps and pipes
Adding the emptying pipe
→ Work, taps and pipes

Test yourself on Arithmetic Reasoning

20 past SSC CGL questions from this chapter, timed at 12 minutes and marked the way the exam marks it. You see your score and every answer the moment you finish. Free to start.

Take the Arithmetic Reasoning chapter test Drill all 11 questions