Part 8

19. A man had a certain number of £’s, which he divided among 4 men. To the first he gave a part, to the second one-third of what was left after the first’s share, to the third he gave five-eighths of what was left, and to the fourth the balance, which equalled two-fifths of the first man’s share. How much money did he have, and how much did each receive, none receiving as much as £20?

ROWING AGAINST TIME.

20. In a time race, one boat is rowed over the course at an average pace of 4 yards per second, another moves over the first half of the course at the rate of 3½ yards per second, and over the last half at 4½ yards per second, reaching the winning post 15 seconds later than the first. Find time taken by each.

STOCK-BREEDING.

21. A farmer, being asked what number of animals he kept, answered: “They’re all horses but two, all sheep but two, and all pigs but two.” How many had he?

A QUIBBLE.

22. What is the difference between twice one hundred and five, and twice one hundred, and ten?

23. The product of two numbers is six times their sum, and the sum of their squares is 325. What are the numbers?

THE PUZZLE ABOUT THE “PER CENTS.”

There are many persons engaged in business who often become badly mixed when they attempt to handle the subject of per centages. The ascending scale is easy enough: 5 added to 20 is a gain of 25%; given any sum of figures the doubling of it is an addition of 100%. But the moment the change is a decreasing calculation the inexperienced mathematician betrays himself, and even the expert is apt to stumble or go astray. An advance from 20 to 25 is an increase of 25%; but the reverse of this, that is, a decline from 25 to 20 is a decrease of only 20%.

There are many persons, otherwise intelligent, who cannot see why the reduction of 100 to 50 is not a decrease of 100%, if an advance from 50 to 100 is an increase of 100%.

The other day, an article of merchandise which had been purchased at 10 pence a pound was resold at 30 pence a pound--an advance of 200%. Whereupon, a writer in chronicling the sale said that at the beginning of the recent depression several invoices of the same class of goods which had cost over 30 pence per pound had been finally sold at 10 pence per pound--a loss of over 200%! Of course there cannot be a decrease or loss of more than 100%, because this wipes out the whole investment and makes the price nothing. An advance from 10 to 30 is a gain of 200%; but a decline of 30 to 10 is a loss of only 66⅔%.

A very deserving trader was ruined by his miscalculations respecting mercantile discounts. The article he manufactured he at first supplied to retail dealers at a large profit of about 30%. He afterwards confined his trade almost exclusively to large wholesale houses, to whom he charged the same price, but allowed a discount of 20%, believing that he was still realising 10% for his own profit. His trade was very extensive, and it was not till after some years that he discovered the fact that in place of making 10% profit, as he imagined, by this mode of making his sales he was realising only 4%. To £100 value of goods he added 30%, and invoiced them at £130. At the end of each month, in the settlement of accounts amounting to some thousands of pounds with individual houses, he deducted 20%, or £26 on each £130, leaving £104, value of goods at prime cost, instead of £110, as he all along expected.

24. Divide 75 into two parts so that three times the greater may exceed seven times the less by 15.

25. What number is that which, being divided by 7 and the quotient diminished by 10, three times the remainder shall be 24?

N.B.

“Trust men and they will trust you,” said Emerson. “Trust men and they will bust you,” says the business man.

26. Two years ago to Hobart-town A certain number of folk came down. The square root of half of them got married, And then in Hobart no longer tarried; Eight-ninths of all went away as well (This is a story sad to tell): The square root of four now live here in woe! How many came here two years ago?

PECULIARITIES OF SQUARES.

The following is well worth examining:--

2^2. equals 1 plus 2 plus 1 equals 4 3^2. " 4 " 2 " 3 " 9 4^2. " 9 " 2 " 5 " 16 5^2. " 16 " 2 " 7 " 25 6^2. " 25 " 2 " 9 " 36 7^2. " 36 " 2 " 11 " 49 8^2. " 49 " 2 " 13 " 64 9^2. " 64 " 2 " 15 " 81 10^2. " 81 " 2 " 17 " 100 11^2. " 100 " 2 " 19 " 121 12^2. " 121 " 2 " 21 " 144

27. How many inches are there in the diagonal of a cubic foot? and how many square inches in a superficies made by a plane through two opposite edges of the cube?

FATHER (who has helped his son in his arithmetic at home)--“What did the teacher remark when you showed him your sums?”

JOHNNY--“He said I was getting more stupid every day.”

A “CATCH.”

28. 2 plus 2 = 4 2 x 2 = 4 The sum and product are alike.

Find another number that when added to itself the sum will equal its square.

29. A man went to market with 3 baskets of oranges, which he sold at 6d. per dozen; after paying 2s. for refreshments and his coach fare, he had remaining 7s. The contents of the first and second baskets were equal to four times the first, and the contents of the first and half the third were together equal to the second; if he had sold the second and third baskets at 4d per dozen, he would have made as much money as he had now remaining. What was the coach fare?