X gives Y a start of $40$ m.

It means when X completes $1000$ m, Y will complete $960$ m.

Speed of X : Speed of Y = $1000 : 960$

Speed of X : Speed of Y = $25 : 24$ ----------(1)

X gives Z a start of $64$ m.

It means when X completes $1000$ m, Z will complete $936$ m.

Speed of X : Speed of Z = $1000 : 936$

Speed of X : Speed of Z = $125 : 117$ ------------(2)

Combining equations (1) and (2), we get

X : Y : Z = $125 : 120 : 117$

Speed of Y : Speed of Z = $120 : 117$

Speed of Y : Speed of Z = $40 : 39$

The speed-distance ratio will be equal for Y and Z.

Y = $25 \times 39$

Y = $975$

So when Y finishes $1000$m, Z will complete $975$ m.

It means Y will give Z a headstart of $25$ m.