A man rows to a place 60 km distant and back in 13 hours 30 minutes. He finds that he can row 5 km with the stream in the same time as he can row 4 km against the stream. Find the rate of the stream.

Let the speed of man in still water = m

rate of stream = s

Given, man can row 5 km with the stream in the same time as he can row 4 km against the stream

$$=$$> $$\frac{5}{m+s}=\frac{4}{m-s}$$

$$=$$> $$5m-5s=4m+4s$$

$$=$$> $$m=9s$$

Man rows to a place 60 km distant and back in 13 hours 30 minutes

$$=$$> $$\frac{60}{m+s}+\frac{60}{m-s}=13+\frac{1}{2}$$

$$=$$> $$\frac{60}{9s+s}+\frac{60}{9s-s}=\frac{26+1}{2}$$

$$=$$> $$\frac{60}{10s}+\frac{60}{8s}=\frac{27}{2}$$

$$=$$> $$\frac{6}{s}+\frac{15}{2s}=\frac{27}{2}$$

$$=$$> $$\frac{12+15}{2s}=\frac{27}{2}$$

$$=$$> $$\frac{27}{2s}=\frac{27}{2}$$

$$=$$> $$s=1$$

$$\therefore\ $$Rate of stream = 1 km/hr

Hence, the correct answer is Option B