A, B and C are in a cycle race of 1500 meters. A cycles twice as fast as B, C cycles $\frac{1}{2}$ as fast as B. C completes the race in 40 minutes. Then, where was B from the finishing line when A finished the race?

750 m from the finish line

ATQ,

Ratio of Speed:

A : B = 2 : 1

B : C = 2 : 1

⇒ A : B : C = 4 : 2 : 1

Note: when time is same, then ratio of speed is directly proportional to distance

Therefore, Distance Ratio:

⇒ A : B : C = 4 : 2 : 1

A cycles = 4R = 1500 m

1R = 375,

then B cycles = 2R = 2 × 375 = 750 m

Therefore, when A finish the 1500m race, that time B will be at 750 m from the finishing line.

Alternate:

Speed ratio = Distance ratio:

A : B = 2 : 1

It means B cycles half of A, therefore, when A cycles 1500m at that time B cycles 750m.

Hence, when A finish the 1500m race, that time B will be at 750 m from the finishing line.