GATE 2022 EE GA Q.2: solution and answer

GATE 2022 · EEGA Q.2 · 1 mark · MCQ

In a 500 m race, P and Q have speeds in the ratio of $3 : 4$ . Q starts the race when P has already covered 140 m.

What is the distance between P and Q (in m) when P wins the race?

(A)
20
(B)
40
(C)
60
(D)
140

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Answer and solution

ANSWER

When P wins, Q has covered 480 m, so the distance between P and Q is 20 m: option (A).

Official answer: ASource: Official answer key, GATE 2022 EE (IIT Kharagpur)

From the moment Q starts until P finishes, P runs the rest of the race: $500 - 140 = 360 m$ .
Over this stretch P and Q run for the same time, so the distances they cover are in the ratio of their speeds: $\frac{d _{Q}}{d _{P}} = \frac{v _{Q}}{v _{P}} = \frac{4}{3}$ .
So while P runs its last 360 m, Q covers $d_{Q} = 360 \times \frac{4}{3} = 480 m$ .
When P finishes, P is at the 500 m mark and Q is at the 480 m mark (Q started from the start line). The gap is $500 - 480 = 20 m$ .
Check: $480 < 500$ , so Q has not yet finished and P does win. The distance between P and Q is 20 m, option (A).

KEY IDEA

If two runners run for the same length of time, the distances they cover are in the same ratio as their speeds. Only count the stretch where both are running, which starts when Q sets off after P has already covered 140 m.

WATCH OUT FOR

Using the full 500 m for P (Q would then cover about 666.7 m, which is impossible), or subtracting the head start twice. Another slip is answering 140 m, which is P's head start and not the gap at the finish.

From the GATE 2022 EE paper. Every question of this paper · Download the full paper · All 58 Numerical questions, with notes

GATE 2022 EE GA Q.2: solution and answer

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