An officer wishing to arrange his men in a solid square found by his first arrangement that he had 39 men left over. He then started increasing the number of men on a side by one, but found that 50 additional men would be needed to complete a new square.
How many men did the officer have?
The officer had 1975 men. When he formed a square measuring 44 by 44, he had 39 men over. When he tried to form a square 45 x 45, he was 50 men short.
Find four numbers, the sum of which is 45, so that if 2 is added to the first number, 2 is subtracted from the second number, the third number is multiplied by 2 and the fourth number is divided by 2, then the four numbers so produced are all the same. What are the four numbers?
Jack had only $2, but he needed $3 for his cab fare home. He went to a pawn shop and pawned his $2 for $1.50. Jack then bumped into Don and told him that he would sell him his $2 pawn ticket for $1.50. Dan agreed. Since Jack started out with $2, and he ended up with $3, who is out the extra dollar and why?
Don is out the extra dollar. Before the pawn broker will return the $2 to the ticket holder, he will want the $1.50 which he advanced returned to him. Don will give the pawn broker the ticket and the $1.50, and the pawn broker will then return the $2.
Mr. Grumper grumbles about bad time-keeping trains like everybody else. On one particular morning he was justified, though. The train left on time for the one hour journey and it arrived 5 minutes late. However, Mr. Grumper's watch showed it to be 3 minutes early, so he adjusted his watch by putting it forward 3 minutes. His watch kept time during the day, and on the return journey in the evening the train started on time, according to his watch, and arrived on time, according to the station clock. If the train traveled 25 percent faster on the return journey than it did on the morning journey, was the station clock fast or slow, and by how much?
The station clock is 3 minutes fast. The morning journey took 65 minutes, and the evening journey therefore took 52 minutes, and the train arrived 57 minutes after it should have left, that is, 3 minutes early.
Two wine merchants arrive at the gates of Paris. One has 64 and the other 20 barrels of wine. Since they have not enough money to pay the custom duties, the first pays 40 francs and 5 barrels of wine. The second pays 2 barrels of wine but receives 40 francs in change.
What is the value of each barrel of wine and what is the duty payable?
The value of a barrel is 120 francs and the duty is 10 francs a barrel.