Two locations A and B are at diametrically opposite ends of a circular track. Rekha starts running along the track from location A in the clockwise direction. Sajal starts running simultaneously along the track in the anticlockwise direction from location B. If the length of the circular track is 14 km, and the speeds of Rekha and Sajal are in the ratio 5: 2, then the distance, in km, travelled by Rekha, when they meet at location B for the first time, is

Track 14 km; A and B diametrically opposite, so 7 km along the track between A and B. Let speeds be $$5x$$ (Rekha, clockwise from A) and $$2x$$ (Sajal, anticlockwise from B).

Rekha is at B at times $$t = (7 + 14k)/(5x)$$ for $$k = 0, 1, 2, \ldots$$

Sajal is at B at times $$t = 7m/x$$ for $$m = 1, 2, \ldots$$

Set equal: $$(7 + 14k)/(5x) = 7m/x \Rightarrow 1 + 2k = 5m$$. Smallest valid: $$m = 1, k = 2 \Rightarrow t = 7/x$$.

Rekha covers $$5x \cdot 7/x = \mathbf{35}$$ km.