129.I ran to a certain railway station to meet the train which was due at 3.15 p.m. When I arrived on the platform the hands of the clock made equal angles with 3 o’clock. How long had I to wait?
130.The wall of China is 1500 miles long, 20 feet high, 15 feet wide at the top and 25 at the bottom. The largest of the pyramids is said to have been 741 feet at the base, 481 feet vertical when finished. How many such pyramids could be built out of the wall of China?
GRAMMAR.
Schoolmaster—“Now, boys, the word ‘with’ is a very bad word to end a sentence with.”
131.There is an arch of quadrantal form; the rise of the crown is 17 feet. What is the span?
132.
Two pairs of fives I bid you take,And four times four and forty make.
Two pairs of fives I bid you take,And four times four and forty make.
133.A lady bought a quantity of flannel, which she distributed among some poor women; the first received 2 yards, the second 4 yards, and so on; the lot cost her £5 14s. 2½d. How many women were there, and what did the lady pay per yard?
134.A and B marry, their respective ages being in proportion to 3 and 4. Now after they have been married 14 years their ages are as 5 to 6, and the age of A is 5 times that of her youngest child, who was born when the parents’ ages were as 4 to 5. Required: the ages of A and B when they were married, and the age of the youngest child now that they have been married 14 years.
AN APPALLING “SUM.”
At a school, a short time back, the pupils were given, as a home lesson, the task of subtracting from 880,788,889 the number 629 so often till nothing remained.
The boys worked on for hours without any perceptible diminution of the figures, and at length gave up the task in despair. Some of the parents then tried their hands, with no better success. For, in order to work out the sum, the number 629 would have to be subtracted 1,400,300 times, leaving 189 as a remainder.
Working 12 hours a day, at the rate of 3 subtractions per minute, it would take over 1 year and 9 months to complete the sum which had been set the poor lads for their home lesson.
A MILITARY LUNCHEON.
135.A certain number of Volunteers—namely, Commissioned Officers, Non-commissioned Officers, and Privates had a dinner bill to pay; there were, it seemed, half as many more Non-Com. Officers as Com., one-third as many more Privates as Non-Com. Officers, and they agreed that each Commissioned Officer should pay one-third as much again as each Non-Com., and each Non-Com. one-fifth as much again as each Private; but 1 Commissioned and 2 Non-Com. Officers slipped away without paying their portion (5s.), each of the others had to pay in consequence 4d. more. What was the amount of the bill, and the number of each present?
Twice the half of 1½? Ask your friends—it bothers them.
The Problem Easily Solved.
“Do you see that row of poplars on the other bank standing apparently at equal distances apart?” asked a grave-faced man of a group of people standing by a river.
The group nodded assent.
“Well, there’s quite a story connected with those trees,” he continued. “Some years ago there lived in a house overlooking the river a very wealthy banker, whose only daughter was beloved by a young surveyor. The old man was inclined to question the professional skill of the young rod and level, and to put him to the test directed him to set out on the river shore a row of trees, no two of which should be any further apart than any other two. The trial proved the lover’s inefficiency, and forthwith he was forbidden the house, and in despair drowned himself in the river. Perhaps some of you gentlemen with keen eyes can tell me which two trees are furthest apart?”
The group took a critical view of the situation, and each member selected a different pair of trees. Finally, after much discussion, an appeal was made to the solemn-faced stranger to solve the problem.
“The first and the last,” said he, calmly, resuming his cigar and walking away with the air of a sage.
136.
Twice five of us are eight of us, and two of us are three,And three of us are five of us—now how can all this be?If that does not puzzle you I’ll tell you one thing more:Eight of us are five of us and five of us are four.
Twice five of us are eight of us, and two of us are three,And three of us are five of us—now how can all this be?If that does not puzzle you I’ll tell you one thing more:Eight of us are five of us and five of us are four.
“EXPRESSIONAL” MEASURES.
The table of measures says that 3 barleycorns make 1 inch—and so they do. When the standards of measures were first established 3 barleycorns, well-dried, were taken out and laid end to end, and measured an inch.
The “hairbreadth” now used indefinitely for infinitesimal space, was a regular measure, 16 hairs laid side by side equalling 1 barleycorn.
The expression “in a trice,” as everyone knows, means a very short space of time. The hour is divided into 60 minutes, the minute into 60 seconds, and the second into 60 “trices.”
A CHALLENGE.
137.A lady belonging to the W.C.T.U. was endeavouring to persuade a gentleman friend of hers to give up the drink; he replied, “I will sign the pledge if you tell me how many glasses of beer did I drink to-day if the difference between their number and the number of times the square root of their number is contained in 2 be equal to 3.”
MEMORY SYSTEM.
Teacher—“In what year was the battle of Waterloo fought?”
Pupil—“I don’t know.”
Teacher—“It’s simple enough if you only would learn how to cultivate artificial memory. Remember the twelve apostles. Add half their number to them. That’s eighteen. Multiply by a hundred. That’s eighteen hundred. Take the twelve apostles again. Add a quarter of their number to them. That’s fifteen. Add to what you’ve got. That’s 1815. That’s the date. Quite simple, you see, to remember dates if you will only adopt my system.”
A GLOBE TROTTER.
138.Everyone knows that in a race on a circular track the competitor who has the “inside” running has the least ground to cover, hence the great desire of cyclists, jockeys, &c., to “hug the fence.”
Now a gentleman, six feet high, starts walking round the Earth on the equator; his feet, therefore, have the inside running. Find out how much further his head travels than his feet in performing this wonderful journey? taking the circumference of the globe at the equator to be 25,000 miles.
Precocious Juvenile—“Mamma, it isn’t good grammar to say ‘after I,’ is it?”
His Mother—“No, Georgie.”
Precocious Juvenile—“Well, the letter J comes after I. Which is wrong—the grammar or the alphabet?”
139.There is an island in the form of a semi-circle; two persons start from a point in the diameter; one walks along the diameter, and the other at right angles to it; the former reaches the extremity of the diameter after walking 4 miles, and the latter the boundary of the island after walking 8 miles. Find the area of the island.
140.There is a certain number consisting of three figures which is equal to 36 times the sum of its digits, and 7 times the left-hand digit plus 9, equal to 5 times the sum of the remaining digits, and 8 times the second digit minus 9 is equal to the sum of the first and third. What is the number?
141.A bottle and cork costs 2½d.; the bottle costs 2d. more than the cork. What is the price of each?
A Cure for Big Words.
Here is a good story of how a father cured his son of verbal grandiloquence. The boy wrote from college, using such large words that the father replied with the following letter:—“In promulgating your esoteric cogitations, or articulating superficial sentimentalities, and philosophical or pscyhological observations, beware of platitudinous ponderosity. Let your conversation possess a clarified conciseness, compacted comprehensibleness, coalescent consistency, and a concatenated cogency. Eschew all conglomerations of flatulent garrulity, jejune babblement, and asinine affectations. Let your extemporaneous descantings and unpremeditated expatiations have intelligibility, without rhodomontade or thrasonical bombast. Sedulously avoid all polysyllabical profundity, pompous prolixity, and ventriloquial vapidity. Shun double entendre and prurient jocosity, whether obscure or apparent. In other words,speak truthfully, naturally, clearly, purely, but do not use big words.”
142.With a pair each of four different weights, 1 lb. up to 170 lbs. can be weighed. What are the weights?
143.A man going “on the spree” spends on the first day 10s. 5d., the second 18s., the third £1 8s. 7d., the fourth £2 2s. 8d., and so on at that rate of increase until he has spent all he had—£183 6s. 8d. How many days was he on the spree?
144.Divide one shilling into two parts, so that one will be 2½d. more than the other.
COMPLIMENTARY, VERY!
Editor—“Did you see the notice I gave you yesterday?”
Shopkeeper—“Yes, and I don’t want another. The man who says I’ve got plenty of grit, and that the milk I sell is of the first water, and that my butter is the strongest in the market, may mean well, but he is not the man whose encomiums I value.”
145.A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons, and then filling the same vessel with water draws off the same quantity of liquor as before, and so on for four draughts, when only 81 gallons of pure wine is left. How much wine did he draw each time?
146.A man has 4 horses, for which he gave £80; the first horse cost as much as the second and half of the third, the second cost as much as the fourth minus the cost of the third, the third cost one-third of the first, and the fourth cost as much as the second and third together. What was the price of each horse?
The Divided Pound.
147.A father wishes to divide £1 between his four sons, giving one-third to one, one-fourth to another, one-fifth to another, and one-sixth to another; in doing so he finds he has only disbursed 19s.; the balance, 1s., is then divided in the same proportion. What amount does each receive in full in the proportion named?
RAILWAY-SHUNTING PUZZLE.
148.A locomotive is on the main line of railway; the trucks marked 1 and 2 are on sidings which meet at the points, where there is room for one truck only and not for the locomotive. It is desired to reverse the position of the trucks—that is, put 1 where 2 is, and 2 where 1 is, and yet leave the locomotive free on the main line. This must be done by means of the locomotive only, either pulling or pushing the trucks—it may be between them, thus pulling one and pushing the other—but no truck must move without the locomotive.
In working this puzzle out, it would be best to draw the diagram on an enlarged scale, and have articles to represent the trucks and locomotive.
149.In a public square there is a fountain containing a quantity of water; around it stand a group of people with pitchers and buckets. They draw water at the following rate: The first draws 100 quarts and one-thirteenth of the remainder, the second 200 quarts and one-thirteenth of the remainder, the third 300 quarts and one-thirteenth, and so on, until the fountain was emptied. How many quarts were there in the fountain?
ENGLISH FROM A GERMAN MASTER.
Prof. Goldburgmann—“Herr Kannstnicht, you will the declensions give in the sentence, “I have a gold mine.”
Herr Kannstnicht—“I have a gold mine; thou hast a gold thine; he has a gold his; we, you, they have a gold ours, yours, or theirs, as the case may be.”
Prof. Goldburgmann—“You right are; up head proceed. Should I what a time pleasant have if all Herr Kannstnicht like were!”
SPENDING THEIR “ALL.”
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?
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 theproblem out, boys.Chorus of Pupils.Oh! dear! no!We readily believe it, Sir! sinceyousay so!
· 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 theproblem out, boys.Chorus of Pupils.Oh! dear! no!We readily believe it, Sir! sinceyousay so!
· 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 theproblem out, boys.
Chorus of Pupils.Oh! dear! no!We readily believe it, Sir! sinceyousay 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.
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.
Two-thirds of six is nine, one-half of twelve is seven,The half of five is four, and six is half of eleven.
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?
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.
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 letterI.
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 roundThat he may graze over just one acre of ground?
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 roundThat 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.
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 thatwell kept booksare 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 manwithoutbooks 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:—
“Whosebeer 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.
The well known author of several works on account-keeping, Mr. Yaldwyn, tells a rather good thing which actually occurred in New Zealand some time back. Mr. Yaldwyn was at the time engaged examining the books in one of the offices in a country town, and enquired from one of the clerks standing near if the ledger were posted. The person appealed to answered that “he didn’t know,” whereupon Mr. Y. said that he required it done, and with as little delay as possible. A few minutes later the same individual came rushing in and informed him that the ledger was “posted.” Such a piece of “lightning book-keeping” so surprised Mr. Y. that he further questioned the man, who replied “You said you wanted the ledger posted, and, begorra, I posted it.” It then dawned upon Mr. Yaldwyn that the clerk, who was an Irishman, had actuallypostedthe book in the post office!
THEY MANAGED IT.