Final answer:
The minister exposed the old lady by cleverly replacing an important letter she wished to keep secret with one of his own, demonstrating his cunning and boldness.
Step-by-step explanation:
The minister succeeded in exposing the old lady by employing a clever and deceitful tactic. During a conversation, the minister, known as Minister Dā, noticed a letter that the old lady wished to keep secret.
Recognizing the importance of the letter from its handwriting, he slyly replaced it with a letter of his own, taking the important one without the old lady being able to protest in the presence of another exalted personage. This act demonstrated his daring and ingenuity, and it left a significant impression on the person wronged, as she was unable to call attention to the theft.