Question

On a topographical map drawn to a scale of $1:100,000$, a hill summit is marked with a spot height of $520\text{ m}$. The terrain features uniform contour intervals of $20\text{ m}$. Point $X$ is located on the fifth contour line directly below the summit. Point $Y$ is situated at a lower elevation such that the vertical difference in height between Point $X$ and Point $Y$ is $240\text{ m}$. If the straight-line distance measured between Point $X$ and Point $Y$ on the map is $6\text{ cm}$, calculate the average gradient between Point $X$ and Point $Y$ expressed in the ratio $1 : n$. What is the value of $n$?