INTELLECT SHARPENERS.

New Zealand Herald, Volume LXV, Issue 19932, 28 April 1928, Page 5 (Supplement)

INTELLECT SHARPENERS.

BT 5t £. BBITQJJ.

Headers are requested not to send in their solutions unless these arß specially asked for, but to keep them for comparison with those published on thtt Saturday following the publication of the problems.

SHOP SALES. If a shopkeeper sells a pair of boots fcr thirty shillings, which cost him twenty shillings, ho will no doubt assure the customer who has suggested that the pro- | fit is 50 pep cent., that it is really only 33 1-3 per cent. This method of arriving. ' at this conclusion is that his calculation is made on the selling price instead of on the cost, for a trader seas nothing illogical or unmathematical in calculating the percentage of profit on capital—ten shillings in this case—that was never invested nor becomes the seller's until after a sale is effected. A problem on trading profits may give the reader an instance of how percentages can appear what they are not.' A shopkeeper marks an article for sale aifc 33 1-3 per cent, above cost, which during "sale week" is offered at that rate less 10 per cent. What percentage of profit does he get if the article is sold in the course of the "sale," and what did it cost him if he receives twelve shilling!! for it while the discount ii» operative ? AT TWO DIFFERENT SPEEDS. Simple problems not infrequently pro-, duce more discussion and controversy than, those of a complex nature, and o:ae arising from an incident at the recent motorcycle sports is a case in point. A machine* travels once round the inner circumference! of a circular track in exactly three minutes. Half the distance is covered at i> uniform speed of 30 aa.p.h., the car being; then slowed down t l ,<> an even rate of 20 m.p.h. for the remaining half. What isi the exact distance of this track? Tho schoolmaster who related the incident states that there was only one in a littlo gathering of a, dozen discussing the poinii who had correctly given the distance—yet it is absurdly simple and the nonacademic reader is assured that only elementary arithmetic is necessary in solving; it, the ratio of a radius or diameter to circumference, for instance, being wholly irrelevant. DEAL IN BROAD ACRES. A somewhat puzzling transaction in broad acres came under notice recently, and, as it involves a point that perplexed some of the interested parties as well an others who knew the details, the particulars are published in the form of a problem. Two landowners in a wool-produc-ing district who adjoining properties of 6000 and 4000 acres respectively, of equal value an acre, entered into partnership to work the two blocks as on<» holding. They, however, required further capital, so a third partner was brought in, the sum of £IO,OOO being paid by him for one-third share in the concern. The point that is still being discussed is how shcmld the £IO,OOO he divided between the two original owners, who are to be <iia equal shares with the third partner. Some little thought is required to solve it, for there are people of experience in finance, who cannot agree as to what the amounts should be. But there is inlwone way in which the sum can be equitably allotted. Can the reader determine this? MILK AND WATER. It is a well-accepted axiom that judges and magistrates decide every case according; to its merits, so that when we read of a dairyman, whose milk was found to contain one-half per cant, of added water, having been admonished and discharged, he was proba,bly dealt with as equitably as his rival, who was fined £2O for adulterating the milk in the following flagrant He first took a measure and put into it pure milk up to exactly one-half its capacity. Into another vessel of just twice the size more pure milk was poured to the extent of exactly one-third of its capacity. He then filled each vessel with water, pouring the contents of both into a large can. This procedure was followed until all. the milk, as taken from the cows, had been similarly dealt with. Can the reader say what were the proportions of milk and water in the product when found in this condition by the inspector, and how much adefed water would there be in five gallons oif the mixture ? PROFITS OF ADDED WATER.

The previous problem prompts another on the same subject, but which, however, concerns the profits that unscrupulous tradesmen are liable to make by such fraudulent practices. For examplu, a milk vendor buys pure milk from a farmer at lid per gallon, and, after diluting it with water, sells the mixture at 3£d pur quart. When the inspector had it analysed ifc was found that the proportion of milk to water was as 28 is to 5. What profit would this milkman make in a week if his total expenditure-for pure milk during that period was £ll 10a at the price quoted, and that, after adulterating it in the manner stated, he sold the mixture afc per quart, ? LAST IffEEK'S SOLUTIONS. The Scheme of Leap Yeats. As pointed out, a new century does not commence in a century year, e.g., in 1900 or 2000, but on the first day in the following year, viz., 1901 and 2001. This .must not be overlooked if the reader desires to test tho method of ascertaining the day of the week that a new century commences on, or the day on which February 29 fall 3 in any leap year. An Unreliable Clock. The suburban post office clock must hav«j been five minutes fast. Two Clerks' Salaries. If Brown paid Jones 5s 6d out of his lafth year's salary, which amount the latifcer added to his, their receipts for that year would be the same, viz., £l2l 5s bd. By Two Roads. The road from X to Te Puta is 10 miles and consequently the distance lrom that point to Otepi is 53 miles. A Flexible Tape 'Measure. There would be exactly 158 complete turns in the coil when rolled in the ma nner stated. ANSWERS TO CORRESPONDENTS!. R.G.—That is one of the common fallacies, bat the explanation given leaves no room for doubt. W.M.B.—It is a centuiy-old problem s but still now, and "keen readers" there will no doubt aiways be who are at firs! puzzled by it. In another form it nmy be published later on. C.H.L.—The rule is that when four sidej are in arithmetical progression, the great)