Explanation:

- In the race, X beats Y by 100 meters, meaning when X finishes 1500 meters, Y has run 1400 meters.

- X also beats Z by 240 meters, so when X finishes 1500 meters, Z has run 1260 meters.

- To find the distance by which Y beats Z, determine how far Z has run when Y finishes.

- Z runs 1260 meters while X runs 1500 meters.

- Therefore, when Y runs 1400 meters, calculate Z's equivalent distance using proportions:

$$

\frac{1260}{1500} \times 1400 = 1176 \text{ meters}

$$

- So, Y beats Z by $1400-1176=224$ meters.

None of the options match 224 m, highlighting a mistake in the problem or options provided.