Part 7
150. Three men going “on the spree” decide to spend all their money. The first, A, “shouts” for the company and then gives his balance to B, who also in turn pays for 3 drinks and gives his balance to C, who can then just manage to pay for drinks once more at 6d. each. How much money had each?
151. There is a regiment of 7300 soldiers, which is to be divided into 4 companies--half of the first company, two-thirds of the second, three-quarters of the third, and four-fifths of the fourth--to be composed of the same number of men. How many soldiers are there in each company?
A GRAVE MISTAKE.
A Scotch tradesman, who had amassed, as he believed, £4000, was surprised at his old clerk’s showing by a balance-sheet his fortune to be £6000. “It canna be--count again,” said the old man. The clerk did count again, and again declared the balance to be £6000. Time after time he cast up the columns--it was still a 6, and not a 4, that rewarded his labours. So the old merchant, on the strength of his good fortune, modernised his house, and put money in the purse of the carpenter, the painter, and the upholsterer. Still, however, he had a lurking doubt of the existence of the extra £2000; so one winter’s night he sat down to give the columns “one count more.” At the close of his task he jumped up as though he had been galvanised, and rushed out in a shower of rain to the house of the clerk, who, capped and drowsy, put out his head from an attic window at the sound of the knocker, mumbling, “Who’s there, and what d’ye want?” “It’s me, ye scoundrel!” exclaimed his employer. “Ye’ve added up the year of our Lord amang the poons!”
PROBLEM FOR PRINTERS.
152. A book is printed in such a manner that each page contains a certain number of lines, and each line a certain number of letters. If each page contains 3 lines more, and each line 4 letters more, the number of letters in each page will be 224 more than before; but if each page contains 2 lines less, and each line 3 letters less, the number of letters in each page would be 145 less than before. Find the number of lines in each page, and the number of letters in each line.
THE INCOME TAX.
153. The charge on a major income is the same in amount as that on a minor one, which is 2½ per cent. of their mutual difference, but the rate imposed on the overplus of a major income is 4 per cent., so that on a composite income of the major and minor the charge would be £3 8s. Required the major and minor incomes.
“Your Money or Your Life!”
154. Two gentlemen, A and B, with £100 and £48 respectively, having to perform a long journey through a lonely part of the country, agree to travel together for purposes of safety; they are, however, taken unawares by a gang of bushrangers who, calling upon them to “bail up,” ease them of some of their cash. The leader of the gang was satisfied with taking twice as much from A as from B, and left to A three times as much as to B. How much was taken from each?
[Illustration]
GEOMETRICAL MUSIC.
· A point, my boys, is that which has no length, breadth, or dimension. -- A line has length, and yet is but a point drawn in extension. All lines have names expressing some distinguishing particular. As: horizontal, parallel, oblique, and perpendicular. _Chorus of Pupils._ Oh! dear! oh! A pretty science mathematics is to know.
The lines called parallel are those which, drawn in one direction, Continued to infinity, will never make bisection. The thing perhaps sounds odd, but if you entertain a doubt, boys, I’ll draw the lines, ====== now take your slates, and work the problem out, boys.
_Chorus of Pupils._ Oh! dear! no! We readily believe it, Sir! since _you_ say so!
155. In this figure rub out eight lines, and leave two squares. No side nor angle of any square must be left, otherwise that will be counted as a square.
[Illustration]
156. A and B travelled by the same road, and at the same rate from Tamworth to Sydney. A overtook a flock of sheep, which travelled at the rate of three miles in two hours, and two hours after he met a mail coach, which travelled at the rate of nine miles in four hours. B overtook the flock 45 miles from Sydney, and met the coach 40 minutes before he came to the 31-mile post from the Metropolis. Where was B when A reached Sydney?
ENGLISH HISTORY.
A school examination paper contained the question:--“Write down all you know about Henry VIII,” and one of the small boys answered as follows:--
“King Henry 8 was the greatest widower that ever lived. He was born at Anne Domini in the year 1066. He had 510 wives besides children. The first was beheaded and afterwards executed, and the second was revoked. She never smiled again. But she said the word ‘Calais’ would be found on her heart after death. The greatest man in this reign was Lord Sir Garret Wolsey--named the Boy Bachelor. He was born at the age of fifteen unmarried. Henry 8 was succeeded on the throne by his great-grandmother, the beautiful Mary, Queen of Scots, sometimes called Lady of the Lake or the Lay of the Last Minstrel.”
157. Two boys, A and B, run round a ring in opposite directions till they meet at the starting point, their last meeting place before this having been 990 yards from it. If A’s rate to B’s be as 5 to 3, find the distance they have travelled.
THE VALUE OF HOME LESSONS.
Two teachers of languages were discussing matters and things relative to their profession.
“Do your pupils pay up regularly on the first of each month?” asked one of them.
“No, they do not,” was the reply; “I often have to wait weeks and weeks before I get my pay, and sometimes I don’t get it at all. You can’t well dun the parents for the money.”
“Why don’t you do as I do? I always get my money regularly.”
“How do you manage it?”
“It is very simple. For instance, I am teaching a boy French, and on the first day of the month his folks don’t send the amount due for the previous month. In that case I give the boy the following exercise to translate and write out at home:--‘I have no money. The month is up. Hast thou any money? Have not thy parents any money? I need money very much. Why hast thou brought no money this morning? Did thy father not give thee any money? Has he no money in the pocket-book of his uncle’s great aunt?’ This fetches them. Next morning that boy brings the money.”
158. There is a number half of which divided by 6, one-third of it divided by 4, and one-fourth of it divided by 3, each quotient will be 9. What is the number?
QUIBBLE.
159. Two-thirds of six is nine, one-half of twelve is seven, The half of five is four, and six is half of eleven.
SOMETHING EASY.
160. Find a sum of £ s. d. (no farthings) in which the figures, in their order, represent the amount reduced to farthings.
161. Three persons won a “consultation” worth £1,320. If J were to take £6, M ought to take £4, and B £2. What is each person’s share?
“ON THE JOB.”
162. Six masons, four bricklayers and five labourers were working together at a building, but being obliged to leave off one day by the rain, they went to a public-house and drank to the value of 45s., which was paid by each party in the following manner: Four-fifths of what the bricklayers paid was equal to three-fifths of what the masons paid, and the labourers paid two-sevenths of what the masons and bricklayers paid. What did each party of men pay?
[Illustration]
163. In a certain speculation I gained £4 19s. 11¾d. for each pound I expended, and by a curious coincidence I found that £4 19s. 11¾d. was the exact amount I had ventured. Required the amount of capital and profit together.
HIS MAJORITY.
164. “I am not a man, I suppose, till I am 21. How long have I to wait yet, if the cube root of my age eight years hence, added to the cube root of my age eleven years ago would make 5?”
DRAUGHT-BOARD PUZZLE.
165. Place eight men on a draught-board in such a way that no two will be in a line either crossways or diagonally. Of course the two colours on the board must be used.
166. A gentleman, dying, left his property thus: To his wife, three-fifths of his son’s and youngest daughter’s shares; to his son, four-fifths of his wife’s and eldest daughter’s shares; to his eldest daughter, two-sevenths of his wife’s and son’s shares, and to his youngest daughter one-sixth of his son’s and eldest daughter’s shares. The wife’s share was £4,650. What did the gentleman leave, and what did each receive?
SAMSON OUTDONE.
A man boasted that he carried off an entire timber yard in his left hand. It turned out that the timber-yard was a three-foot rule.
Domino Puzzle.
[Illustration]
167. Arrange the 28 dominoes in such a manner as to have two squares of each number; there are eight half-squares of each number in the complete set--eight sixes, eight fives, &c.--so that four of the one number comprise a square. The whole, when finished, will form a figure like a square, resembling a wide letter =I=.
[Illustration]
168. A sum of money is divided among a number of persons; the second gets 8d. more than the first, the third gets 1s. 4d. more than the second, the fourth 2s. more than the third, and so on. If the first gets 6d. and the last £5 2s. 6d., how many persons were there?
IT COULDN’T BE EXPECTED.
Teacher: “Johnny, where is the North Pole?”
Johnny: “I don’t know.”
Teacher: “Don’t know where the North Pole is?”
Johnny: “When Franklin, Nansen and Captain Andrée hunted for it and couldn’t find it, how am I to know where it is?”
169. For a loan of 2,500,000, 4½ per cent. per annum is paid by a mining company whose capital is £4,900,000. The working expenses constitute 52 per cent. of the gross receipts, which amount in the year to £965,000, and the directors set apart £44,450 as a reserve fund. What yearly dividend do the shareholders receive?
170. If a monkey climbs a greasy pole 10 ft. high, ascending 1 ft. with each movement of his arms, and slipping back 6 in. after each advance; how many movements would he have to make, to touch the top, and what height would he have climbed in all?
171. Find two numbers whose G.C.M. is 179, L.C.M. 56385, and difference 10382.
172. What is the difference between twenty four-quart bottles, and four and twenty quart bottles?
THE G.C.M.
The Greatest Common Measure--A “long pint.”
173. There are two casks, one of which holds thirty gallons more than the other. The larger is filled with wine, the smaller with water. Ten gallons are taken out of each: that from the first is poured into the second; the operation is repeated, and it is now found that the larger cask contains 13 gallons of water. Find the contents of each cask.
174. In the midst of a paddock well stored with grass, I engaged just an acre to tether my ass; What length must that cord be, in grazing all round That he may graze over just one acre of ground?
175. If three first-class cost as much as five second-class tickets for a journey of 100 miles, the total cost of the eight tickets being £3 2s. 6d., find the charge per mile for each first-class and second-class ticket.
HUMILITY.
In a certain street are three tailors. The first to set up shop hung out this sign--“Here is the best tailor in the town.” The next put up--“Here is the best tailor in the world.” The third simply had this--“Here is the best tailor in this street.”
“On the Wallaby.”
176. Four sundowners called at a station and asked for rations. “Well,” said the manager, “I have a job that will take 200 hours to complete; if you want to do it, you can divide the work and the money among yourselves as you see fit.” The sundowners agreed to do the work on these conditions. “Now, mates,” said the laziest of them, “it’s no good all of us doing the same amount of work. Let’s toss up to see who shall work the most hours a day, and who the fewest. Then let each man work as many days as he does hours a day.” This was agreed to; but the proposer took good care that chance should designate him to do the least number of hours of work. How were the 200 hours put in so that each man should work as many hours as days, and yet no two men work the same number of hours?
177. On multiplying a certain number by 517 a result is obtained greater by 7,303,535 than if the same number had been multiplied by 312. How much greater still would be the result if 811 were the multiplier instead of 312?
A “CATCH.”
178. Six ears of corn are in a hollow stump. How long will it take a squirrel to carry them all out if he takes but three ears a day?
NUMBER 7.
The number 7 has always been considered the most sacred of all our figures. Its prominence in the Scriptures is very remarkable, from Genesis--where we read that the seventh day was consecrated as a day of rest and repose--to Revelations--where we find the seven churches of Asia; seven golden candlesticks; the book with seven seals; the seven angels with seven trumpets; seven kings; seven thunders; seven plagues, &c., &c., its frequent occurrence is most striking.
The Ancients paid great respect to the seven mouths of the Nile. The seven rivers of Vedic India; seven wonders of the world; seven precious stones; seven notes of music; seven colours of the rainbow, &c., &c. The “Lampads seven that watch the Throne of Heaven” led the Chaldeans to esteem the unit 7 as the holiest of all numbers, thereupon they established the week of seven days, and built their temples in seven stages. The temples and palaces of Burma and China are seven-roofed.
In modern times this number has kept up its reputation. Shakespeare paid special regard to it; the “seven ages” and every multiple of it is supposed to be a critical or important period in one’s life.
A modern philosopher as follows apportions--
MAN’S FULL EXTREME.
7 years in childhood, sport and play, (7) 7 years in school from day to day, (14) 7 years at trade or college life, (21) 7 years to find a place and wife, (28) 7 years to pleasure’s follies given, (35) 7 years to business hardly driven, (42) 7 years for some wild-goose chase, (49) 7 years for wealth, a bootless race, (56) 7 years of hoarding for your heir, (63) 7 years in weakness spent and care, (70) And then you die and go--you know not where.
Very many superstitious and curious ideas have been and still are connected with all our figures. For those interested in this subject see page 146--“How To Become Quick At Figures” (Student’s Edition).
“What’s the difference,” asked a teacher in arithmetic, “between one yard and two yards?” “A fence,” said Tommy Yates. Then Tommy sat on the ruler 14 times.
179. What relation is a woman to me who is my mother’s only child’s wife’s daughter?
THE ADVANTAGES OF SKILFUL BOOK-KEEPING.
If a merchant wishes to get pretty deeply in debt, and then get rid of his liabilities by bankruptcy--if, in fact, he proposes to himself to go systematically into the swindling business, and engage in wholesale pecuniary transactions without a shilling of his own, the first thing he should take care to learn would be the whole art of book-keeping.
From what may occasionally be seen of the reports of the proceedings in bankruptcy, it is found that _well kept books_ are regarded as quite a test of honesty, and though assets may have disappeared or never have existed, though large liabilities may have been incurred without any prospect of payment, the bankrupt will be complimented on the straight look of his dealings, if he has shown himself a good book-keeper.
To common apprehension it would seem that well kept books would only help to show a reckless trader the ruinous result of his proceedings, and that while the man _without_ books might flatter himself that all would come out right at last, the man with exact accounts would only get into hot water with his eyes open. If a man may trade on the capital of others without any of his own, and get excused on the ground that he has kept his books correctly, it is difficult to see why a thief who steals purses, &c., may not plead in mitigation of punishment that he has carefully booked the whole of his transactions.
It would be interesting to know the effect of producing a ledger on a trial for felony, as well as curious to observe whether a burglar would be leniently dealt with on the ground that his house-breaking accounts gave proof of his experience in the science of “double-entry.”
Therefore it would be well for those interested to procure copies of “RE ACCOUNTS” and “ADVANCED THOUGHT ON ACCOUNTS.”
THE FIRM HE REPRESENTED.
A commercial traveller handed a merchant upon whom he had called a portrait of his sweetheart in mistake for his business card, saying that he represented that establishment. The merchant examined it carefully, remarked that it was a fine establishment, and returned it to the astonished and blushing traveller with the hope that he would soon be admitted into partnership.
180. A man and a boy being paid for certain days’ work, the man received 27s., and the boy, who had been absent 3 days out of the time, received 12s. Had the man, instead of the boy, been absent the 3 days they would both have claimed an equal sum. Find out the wages of each per day.
181. The extremes of an arithmetical series are 21 and 497, and the number of terms is 41. What is the common difference?
182. A wine which contains 7½ per cent. of spirit is frozen, and the ice which contains no spirit being removed the proportion of spirit in the wine is increased by 8¾ per cent. How much water in the shape of ice was removed from 504 gallons of the mixture?
THE SHARP SELECTOR.
183. A selector rented a farm, and agreed to give his landlord two-fifths of the produce, but prior to the time of dividing the corn the selector used 45 bushels. When the general division was made it was proposed to give to the landlord 18 bushels from the heap in lieu of the share of the 45 bushels which the tenant had used, and then to begin and divide the remainder as though none had been used. Would this method have been correct?
A GOOD “AD.”
A member of a certain firm appeared in a law court with a complaint that his partner would sell goods at less than cost price, and he desired to have him restrained. The defendant utterly denied the charge, and the case was adjourned for a fortnight. As the plaintiff went out of court he exclaimed in a tragic tone: “Then the sacrifice must still go on!” and “I’ll be ruined!” The story was noised abroad, and the result was that the shop was besieged by customers every day. There the case ended, for at the end of the fortnight the plaintiff failed to appear in court, having accomplished his purpose--advertisement.
184. I give 3 sovereigns for 2 dozen wine at different rates per dozen, and by selling the cheaper kind at a profit of 15 per cent. and the dearer at a loss of 8 per cent. I obtain a uniform price for both. What did each dozen cost me?
185. I have in my garden a shrub that grows 12 inches every day, but during the night it withers off to half the height that it was at the end of the previous day. How much short of 2 feet will it be at the end of a year?
TIT-FOR-TAT.
186. A farmer puts a 3 lb. stone in a keg of butter worth 11d. a pound. The merchant cheats him out of 1 lb. on the weight, and then does him out of 1s. 11d. on calico, tobacco, and a shovel. Who is ahead, and how much?
187. Trains leave London and Edinburgh (400 miles apart) at the same time and meet after 5 hours; the train which leaves London travels 8 miles an hour faster than that which leaves Edinburgh. At what rate did the former travel, and at what speed must the latter travel after they have met, in order that they both may reach their destinations at the same time?
“GOOD ENOUGH!”
“Will you give me a glass of beer, please?” asked a rather seedy-looking fellow with an old but well-brushed coat and almost too shiny a hat. It was produced by the barmaid, frothing over the edge of the tumbler.
“Thank you,” said the recipient, as he placed it to his lips. Having finished it in a swallow, he smacked his lips and said, “That is very good beer--_very_! Whose is it?”
“Why, that Perkins’s----”
“Ah! Perkins’s, is it! Well, give us another glass.”
It was done; and holding it up to the light and looking through it, the connoisseur said:--
“’Pon my word, it is grand beer--clear as Madeira! What a fine color! I must have some more of that; give me another glass.”
The glass was filled again, but before putting it to his lips the imbiber said:--
“_Whose_ beer did you say this was?”
“Perkins’s,” emphatically replied the barmaid.
The contents of the glass was exhausted, as also the vocabulary of praise, and it only remained for the appreciative gentleman to say, as he wiped his mouth and went towards the door:--
“Perkins’s beer, is it! I know Perkins very well; I shall see him soon, and will settle with him for three long glasses of his incomparable brew. Good morning.”
A Conspiracy.
188. Three gentlemen are going over a ferry with their three servants, who conspire to rob them if they can get one gentleman to two of them, or two to three, on either side of the ferry. They have a boat that will only carry two at once, and either a gentleman or a servant must bring back the boat each time a cargo of them goes over. How can the gentlemen get over with all their servants so as to avoid an attack?
189. Find two numbers whose product is equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes?
190. Divide 1400 into such parts as shall have the same ratio as the cubes of the first four natural numbers.
This was the tempting notice lately exhibited in the window of a dealer in cheap shirts: “They won’t last long at this price!”
POSTING THE LEDGER.