Question

In a 1 km race, a beats b by 200 m and c by 360 m. in a race of 500 m, by how many metres would b beat c?

Answer 1

HALF OF 1 KM = 500 M 
  HENCE HALF ALL THE TERMS
IN 500M
 A BEATS B BY 100M AND C BY 180

Answer 2

Given:

Total distance in the race=500m

To find:

The number of metres by which B beats C.

Solution:

B wins over C by 100m.

We are given that the total distance to be covered during the race of A, B, C is 1km or 1000m.

Also, A beats C by 360m and B by 200m.

So, when A completes the 1000m, the meters run by C and B is as follows-

B's distance=1000-200=800m

C's distance=1000-360=640m

Now, the ratio of the meters run by B and C=800:640

=10:8

In B and C's race, let C covers X metres.

So, B's distance=500m

C's distance=X

The ratio of their distances=10:8

On equating,

500:X=10:8

500×8/10=X

50×8=X

400=X

So, B wins over C by (500-X)m.

=500-400

=100m

Therefore, B wins over C by 100m.