Concept:
The median of a grouped frequency distribution is calculated using:
\[\text{Median}=l+\left(\frac{\frac{N}{2}-cf}{f}\right)h\]
where \(l\) is the lower boundary of the median class, \(N\) is the total frequency, \(cf\) is the cumulative frequency before the median class, \(f\) is the frequency of the median class, and \(h\) is the class width.

Step 1: Use the total frequency.
\[180+f_1+34+180+136+f_2+50=685\]
\[f_1+f_2+580=685\]
\[f_1+f_2=105\quad ...(1)\]

Step 2: Identify the median class.
\[\frac{N}{2}=\frac{685}{2}=342.5\]
The median class is \(40-50\). Therefore, \(l=40\), \(cf=180+f_1+34=214+f_1\), \(f=180\), and \(h=10\).

Step 3: Apply the median formula.
\[42.6=40+\left(\frac{342.5-(214+f_1)}{180}\right)10\]
\[2.6=\frac{128.5-f_1}{18}\]
\[46.8=128.5-f_1\]
\[f_1=81.7\]