"An Astrologer's Day" is set around the 1920s. Science of the day was in a period, much like today, of exciting expansion with new science being discovered and new technology being developed from the discoveries. For instance, Einstein discovered the explanation of what is called the photoelectric effect thus winning a Nobel Prize; Siegbahn discovered X-ray spectrometry; and Prince de Broglie discovered that electrons are both waves and particles. Various scientific discoveries like these and earlier ones resulted in new technologies like radio, television, toasters, air conditioners, and vacuum cleaners for "hoovering."
At this time in India, and still evident today, there was a comfortable duality with both astrological and scientific ideas and beliefs viewed as legitimate systems and holding sway in people's lives. For instance, to take an example from the author's own life, when Narayan--a much honored author--met his future wife, they had to overcome a seemingly insurmountable obstacle to their marriage because their astrological horoscopes did not match--meaning they would not be suitable marriage partners (she died early of typhoid fever after only four years of marriage).
Therefore, in India, during the time in which Narayan set and wrote the story, astrology had an important and powerful position in society--even for university educated men and women--as it could govern commonplace and important events in their lives. At the same time, India, having a British based and controlled university system, was participating in scientific research just like the rest of the world. As result of the important place of both traditional astrology and scientific expansion, a positron of comfortable duality existed between astrology and science.