In a 500 m race, the ratio of speeds of two contestants P and Q is 3 : 4. P has a head start of 146 m. Then, P wins by

A 60 m

B 40 m

C 20 m

D 10 m

E 28 m

Correct Answer: Option E

P has a headstart of 146 m.

∴ the distace to be travelled by P = 500 – 145 = 354 m

Both run for the same time during the race.

Distance = speed × time

∵ Ratio of speeds of P : Q = 3 : 4

In equal time, the distance travelled by them will also be in the ratio of their speeds, i.e. 3 : 4.

P needs to travel only 354 m to win the race.

Distance travelled by Q in the time P travels 354 metres \(= \frac{4}{3} \times 354 = 472\;m\)

∴ By the time P finishes the race (i.e. the 500 m mark), Q has covered 472 m. Hence P beats Q by (500 – 472 =) 28 m