A rich merchant had collected many gold coins. He did not want anybody to know about them. One day, his wife asked, "How many gold coins do we have?" After pausing a moment, he replied, "Well! If I divide the coins into two unequal numbers, then 37 times the difference between the two numbers equals the difference between the squares of the two numbers." The wife looked puzzled. Can you help the merchant's wife by finding out how many gold coins.
A teacher gave a student the task of adding ‘N’ natural numbers starting from 1. After a while, the student reported his result as 700. The teacher replied that his result was wrong. The student realized that
he had added one number twice by mistake. Find the sum of the digits of the number which the student had added twice.