There are Senior officers and Secretaries in an office. If $15\text{ Secretaries}$ went on leave, then every Secretary has two Senior officers. After that $45\text{ Senior officers}$ went on leave and now every Senior officer has $5\text{ Secretaries}$. Then find out how many Secretaries were there initially.

Let the initial number of Senior officers be $O$ and the initial number of Secretaries be $S$.
*Condition 1: $15\text{ Secretaries}$ go on leave.**
The remaining number of secretaries is $(S-15)$.
According to the condition, every secretary has $2$ senior officers:

$$\frac{O}{S-15}=2⟹O=2(S-15)⟹O=2S-30\text{— (Equation 1)}$$

*Condition 2: Next, $45\text{ Senior officers}$ go on leave.**
The remaining number of senior officers becomes $(O-45)$.
Now, every senior officer has $5$ secretaries:

$$\frac{S-15}{O-45}=5⟹S-15=5(O-45)\text{— (Equation 2)}$$

Now substitute Equation 1 into Equation 2:

$$S-15=5((2S-30)-45)$$

$$S-15=5(2S-75)$$

$$S-15=10S-375$$

$$375-15=10S-S$$

$$360=9S$$

$$S=\frac{360}{9}=40$$

Thus, there were initially $40\text{ Secretaries}$ in the office.