Linear & Circular Races · Topic 1 of 5

🏁 Beats by Distance / Time

1 exam question type, fully solved

A race is run over one fixed distance, and both runners run for the same length of time — the time the winner takes. That single fact is the master key to the whole chapter: since they share the clock, the faster runner simply gets further, so the ratio of distances they cover equals the ratio of their speeds.

The one rule everything is built on

• Beats by a distance. “A beats B by metres” means that the moment A finishes the full distance , B has only reached . In that shared time the speed ratio is .

• From a speed ratio. If , then when the winner covers the loser covers , so the beat is .

• Beats by seconds. A time gap, not a distance gap. Find the loser's speed, see how far the loser had reached in the winner's time, and the rest of the track is the beat: .

• Chained beats. A beats B by , B beats C by on the same length . Never add: the answer is , always a touch under .

🏃Linear Race SimulatorAnimate the race

Speed A (m/s): 10Speed B (m/s): 8Distance (m): 100B's head start (m): 0

A: 0.0 mB: 0.0 mResult: A wins by 20.0 m = 2.5 s

In a 600 m race A beats B by 60 m. When A finishes, B has run m.

Q1In a 500 m race, A beats B by 50 m. When A finishes, how far has B run?

Q2Speed ratio A : B = 4 : 3 in a 400 m race. By how much does A beat B?

Q3In a 100 m race A beats B by 4 m and B beats C by 5 m. By how much does A beat C (approx)?

📚

Real exam questions — Beats by Distance / Time

1 question types · 5 solved examples from real SSC papers

The whole chapter rests on one idea: in a race both runners share the winner's time, so distance ratio = speed ratio. Master "beats by x metres" first.

How to solve this type

A race is run over a fixed distance

d

, and both runners run for the SAME length of time — the time the winner takes. Because time is shared, distance is proportional to speed: whoever is faster simply gets further in that time.

"A beats B by

x

metres" means: at the instant A crosses the finish line (A has run

d

), B has only reached

d-x

. So in equal time their distances are

d

and

d-x

, giving speed ratio

\dfrac{v_A}{v_B}=\dfrac{d}{d-x}

.

"A beats B by

t

seconds" is a TIME gap, not a distance gap: B needs

t

more seconds to finish. Find the loser's speed, multiply by the winner's time to see how far the loser had reached, and subtract from

d

.

For a chain — A beats B by

x

, then B beats C by

y

over the same length

L

— never just add

x+y

. The beat of A over C is

x+y-\dfrac{xy}{L}

(always a little less than

x+y

In a 1000 m race, X beats Y by 100 m. When X finishes, how far has Y run?

A920 mB875 mC850 mD900 m

Speed ratio of P : Q is 5 : 3. In a 500 m race, by how many metres does P beat Q?

A180 mB200 mC190 mD210 m

In a 1200 m race, Rakesh finishes in 36 s and Rajesh in 40 s. By how much does Rakesh beat Rajesh?

A100 mB110 mC120 mD130 m

In a 1500 m race, A beats B by 100 m, and B beats C by 150 m. By what distance does A beat C?

A240 mB150 mC200 mD100 m

In a 100 m race, A beats B by 10 m and B beats C by 10 m. By what distance does A beat C?

A19 mB18 mC21 mD20 m