GATE 2022 | Maths | GA Question 2

Question

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

Answer 1

Time to complete the race for P is 

 t = D1 / S1 = distance remaining for P / speed ratio of P = 360 / 3x = 120 / x

Now in this time Q had covered the distance is 

D2 = S2 * t = speed ratio of Q * time when P complete the race = (120 / x ) * 4x = 480

when P complete the race, Q will cover 480m distance 

So, distance between P and Q is 500 – 480 = 20m