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Mirth and Dancing
A Few Problems


When Jean and Ailie were bridesmaids at the wedding of their only aunt, Jean was but a fifth of the present age of Ailie, but has now reached twice the age that Ailie was then. If the sum of Jean's and Ailie's ages at the time of the wedding was fifteen years, how long has the aunt been married?


A rope is hung over a pulley and an Englishman and a Scot, of equal weights, are given the two free ends. They are told that the first to reach the pulley and touch it will receive a prize. The Englishman is the better rope-climber and tries, while the Scot is dour and does not try, but he wins. Why?


Macpherson spent the first third of his life in Scotland, and then went to Canada to live there for six years. War broke out, and for the next four years Mac was a soldier. He then married, and spent a ninth of his life with his wife as his chief companion, when a son was born to share his affection. The boy, much to his parents' regret, died when he had only attained a third of the age that his father reached five years later when he passed away. How old was Macpherson when he died?


A man decided to give each of his children, nephews and nieces, assembled to celebrate his silver wedding, a present of twenty-five shillings. Unfortunately the calls on his purse that day had left him in the position of being ten shillings short of the requirements. He was, therefore, reluctantly compelled to change his mind, and make his present a pound. By doing so he found himself with twenty-five shillings left. What had he at first and how many recipients were there?


Four brothers decided to leave Glasgow to start work in London and all adopted different means of travel. Ronald paid 120s. to proceed by aeroplane in 52 hours; Hamish took the train and did the journey in 8 hours at a fare of 50s. 3d.; Ian went by coach, being charged 30s. for an adventure taking 15 hours; and Gordon chose the steamer, which meant a train journey from Glasgow of an hour's duration costing 5s. 10d. and a fine sea trip from Edinburgh of 36 hours costing 32s. 6d. What would you suggest as being the relative values of the brothers as Scotsmen, and, putting that consideration aside, what relative values do you consider they put on their time, if, and it is a very questionable if, the comfort and other considerations were the same?


An express train left London for Glasgow, a distance of 401 miles, at the same time as a parliamentary train left Glasgow to do the opposite journey. The express travelled at an average speed of sixty miles per hour and the other train at half that rate. Which was the nearer to London when they met?


A merchant finds that his capital grows each year by one-third of what is left after he has taken 1000 out of the business each year for his personal expenses. If, at the end of three years' trading, he discovers that his capital has doubled, what sum had he to commence operations?


A hospital showed an increase of 3 per cent in the total number of patients treated during the year. The change was not uniform in the different sections, for the number of in-patients fell by 12 per cent while the out-patients increased by 5 per cent, due to the change in road risks. What was the ratio of the two types of patients?


In railway lines the lengths of metal are not closely butted together, but gaps are left between them. The reason is that allowance must be made for the expansion due to rise of temperature. On the other hand, tramway rails are laid without any such provision and, indeed, are often welded together. Why?


If it takes Campbell 50 per cent longer to do a job of work than Perkins and Murphy could do it in working together, and if it takes Perkins twice as long on the same job as Campbell and Murphy working together, how many times the period taken by Campbell and Perkins in partnership, would it take Murphy to accomplish the job on his own?

N.B. - This is not meant to be funny. It is quite a nice problem.


If anyone told you that he was pursued by rats so big that every dimension was one hundred times the normal, and even though you could see them yourself, you would know they were not real, because no such creatures could ever exist in Nature. Why should they be so regarded?

N.B. - This is a serious question.


If you were told, and it seems to be a fact, that a bullet leaving a rifle does not attain its maximum velocity until it has got a certain number of feet upon its journey, and yet a golf-ball leaves the club and a football leaves the foot on a free kick with the highest speed they ever have in their flight, how would you account for the difference?

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