Solution to 61

 Here was the question 

 "When I got to the station this morning," said Harold Tompkins, at
his club, "I found I was short of cash. I spent just one-half of what I had on my railway ticket, and then bought a nickel's worth of candy. When I got to the terminus I spent half of what I had left and ten cents for a news-paper. Then I spent half of the remainder on a bus and gave fifteen cents to that old beggar outside the club. Consequently I arrive here with this single nickel. How much did I start out with?"

Solution :

Let us use a bottom up approach here. 

Mr. Tompkins (funny name!) had a nickel when he reached his destination. 

Prior to that he gave 15 cents to a beggar .

Before giving money to beggar he had 15+5 = 20 cents.

Before that, he spent half his money for bus ticket. Which means 

20 = half of what he had

Money he had before buying bus ticket = 2*20 = 40 cents

 At the time of reaching bus terminal, he had spent half of what he had+10 cents to purchase newspaper

If he had x cents,

x  - (x/2+10) = 40 

x/2 - 10 = 40 

x = (40+10)*2 = 100 cents

Then he bought nickel's worth of candy .

Before spending 5 cents on candy, he had 105 cents.

He bought a train ticket with half of money he had and then left with 105 cents.

If x was his money 

x - x/2 = 105 

x/2 = 105

x = 210 cents

He had 2 dollars and 10 cents when he started his journey.