When a stretched wire and a tuning fork are sounded together, 5 beats per second are produced when the length of the wire is 95 cm or 100 cm. What is the frequency of the fork?

Let the frequency of the tuning fork be m.
Suppose l1 = 95 cm has frequency n1 and l2 = 100 cm has frequency n2 (< n1)
Now, n1 - m = 5 (i)
m - n2 = 5 (ii)
Adding, we get n1 - n2 = 10 (iii)
Also, n1/n2 = l2/l1 = 100/95
n1 = (100/95)n2
From eqn. (iii), (100/95)n2 - n2 = 10, n2 = 190
From eqn. (ii), m = n2 + 5 = 190 + 5 = 195 Hz.