In a 1500 m race, if vehicle P gives vehicle Q a start of 200 m, then vehicle P wins the race by 8 sec. Alternatively, if vehicle P gives vehicle Q a start of 400 m, the race ends in a dead heat. How long does vehicle P take to run 1500 m?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 07 Dec 2022 Shift 1)

Answer 1

Given:

Distance = 1500 m

Vehicle P gives vehicle Q a start of 200 m, and P wins the race by 8 sec

If vehicle P gives vehicle Q a start of 400 m, the race ends in a dead heat

Formula used:

Speed = Distance / Time

Calculations:

For case 1:

Vehicle P gives vehicle Q a start of 200 m, and P wins the race by 8 sec

⇒ Distance travel by P = 1500 m

⇒ Distance travel by Q = 1500 - 200 = 1300 m

⇒ Speed of vehicle P = \(\frac{1500}{t}\)

⇒ Speed of vehicle Q = \(\frac{1300}{t+8}\)

Now for case 2:

If vehicle P gives vehicle Q a start of 400 m, the race ends in a dead heat

⇒ Distance travel by P = 1500 m

⇒ Distance travel by Q = 1500 - 400 = 1100 m

As the race is end at dead heat, they finish the race at tie or equal time

⇒ Time taken by vehicle P = Time taken by vehicle Q

⇒ \(\frac{1500}{\frac{1500}{t}}=\frac{1100}{\frac{1300}{t+8}}\)

⇒ \(t=\frac{11(t+8)}{13}\)

⇒ 13t = 11t + 88

⇒ 13t - 11t = 88

⇒ 2t = 88

⇒ t = 44 sec

⇒ Hence, The time taken by vehicle P is 44 sec