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.
Can you find a five digit number that, if you place a 9 at the beginning to make a new number, is fours times larger than if you place the 9 at the end instead?
Solution
Let the number is 10000x+1000y+100z+10p+q
now according to the given condition
100000*9+10000x+1000y+100z+10p+q = 100000x+10000y+1000z+100p+10q+9
on solving we get 10000x+1000y+100z+10p+q = (900000-36)/39 = 23076