Two numbers are in the ratio $1:3$ and their HCF is $26$. If one number is $78$, then find the other number.

Let the two numbers be $1x$ and $3x$.
The Highest Common Factor (HCF) of $1x$ and $3x$ is $x$.
Given that $\text{HCF}=26$, so $x=26$.

The numbers are:
First number $=1\times 26=26$
Second number $=3\times 26=78$

We are given that one number is $78$. Therefore, the other number is $26$.