${\mathrm{CH}}_3-{\mathrm{CH}}_2-\mathrm{CO}-{\mathrm{NH}}_2\stackrel{\mathrm{NaOH}/{\mathrm{Br}}_2}{\to }\mathrm{A}$

Aqueous solution of $A$.

•  A will turn red litmus to blue as the A formed by the series of given reactions will be basic.
•  If a basic compound is tested with litmus, it turns red litmus blue and 
• if an acidic compound is tested with litmus, it turns blue litmus red.
•  No change is observed in the case of a neutral compound. The A formed here is ${\mathrm{CH}}_3-{\mathrm{CH}}_2-{\mathrm{NH}}_2$, which is basic. Thus, red litmus will turn blue.

Hence, the correct answer is option B) Turns red litmus to blue.