X, Y and Z are three contestants in a race of 1000 m

X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?

  1. 20
  2. 25
  3. 30
  4. 35

Answer

When X runs 1000 m, Y runs (1000 - 40) m and Z runs (1000 - 64) m

Y runs 960 m and Z runs 936 m.

So, when Y runs 1000 m, Z runs

= 936/960 × 1000 = 975 m

So, start Y gives to Z = 1000 - 975 = 25 m

Alternate Solution

X : Y = 1000 : 960

X : Z = 1000 : 936

So, Y : Z = 960 : 936

Y : Z = 1000 : 975

The correct option is B.