CUTTING STEEL RODS.

Evening Post, Volume CXIV, Issue 122, 19 November 1932, Page 23

CUTTING STEEL RODS.

A contractor took a hundred-weight of steel rods to an engineering shop to bo cut iiito one foot lengths, the rods being each throe feet long, the charge for the cutting being twenty shillings. Oa a later occasion the contractor liad another hundred-weight of -rpds of the same quality and the same thickness as in the first order, but in this case the rods were six feet in length and these had to be .'cut in one foot lengths also. As there were obviously double the number, of rods in the first Order as' in the other, the weight and .tile quality of steel being similar in both instances, the contractor argued, when objecting to.tho second price quoted by the cutter, that the f act that one lot contained rods only half the length of those in the other, should make tho cost of cutting the longer rods precisely'the same as charged in the first job;' particularly he contended, as the total length of steel was the same in both., lots. But the.metalworker could not see the logic of the contractor ?s' argument, and. the reader is .asked to decide.the .point, and find how much. should be charged for the second lot based upon the same rates as'in the first order.;. ■ '...'. MOTHER AND THE GIRLS. ' A ■ problem sent by a reader, F.Si, and published- last month concerning the ages-of four persons* has prompted another ■correspondent "55eno" to for{vard the' following jinizlo. Fifteen years ago Mrs.. Jones* had three children,' Alma, Betty, and,.,Clair, whose combined ages then" totalled exactly half that of the mother. Six -years later, namely in 1923,'" her age was equal to the combined: ages of her children, which, however, included a fourth child, Daisy, who was born during that six-year period. • In the present year, 1932, there arc five children, the1 youngest, Emma, .arriving after 1923,.- and < when - she . was born the mother's age was nine years less than the' unitod" ages: of the other four, Alma's age then being one year less than the ages of ■ Claiir'and Daisy together, while Betty's .arid Daisy's combined, .ages at. .that' time totalled half as much again as.Glair's years. This year (1932) the mother's age is a year less than "twice Alma's, and two years more than Alma's and Betty's together. If Emma's age this year is exactly -one-third, of ,CJair.*s,. and the total of 'the six people one-hundred and nineteen years, what are their respective ages? "Zeno" evidently intends the would-be solver to be supplied with plenty of data, but the reader will no doubt sift it well and use' only the essential details. ] DIVIDED INTO ZONES. Here- is^ a little arithmetical caleula-1 tion which some readers may consider suitable for the armchair, though, it is not a condition. It concerns a recent authorised street collection, in the city, there being seventy-five collectors, though only two-hundred-and-sixty-six pounds was the net.result. The city was ■• divided ; into- four zones;- "A", "B", "C", and "D", twelve of these unselfish, workers being allotted to "A", half -as-inauy -again to "B", two-thirds.-as-many-again to "C", the latter's quota being four-fifths of the number of collectors allotted to the largest zone "D". The results showed that ,'.'B-"-.topped the score both* in the matter of the total amount collected as':well as-the average for each worker, 1 while' "A" had the lowest total though its average wasfSigh. Six collectors in "B" zone receiyed'as much' a?' eight in "A", twelve iri "C" as much as nine in "B" while five in"D" got ,as much, money in.'their boxes.as four | in "C" zone. : How-much did each, section', collect? • ■ • • TWO TOR THE ARMCHAIR. During, training excrciso .a .party of footballer's who had gone leisurely along the road1 ffoin-i"A" to'"B" at the rate of one' mile and a half per hour, returned by the samea'oute at a "jogtrot,"'keeping an even, rate1 of travelling of six:miles per. hour.' There was no perceptible delay-on the road, and the question is if the ■ joUrney from. "A" ,to "B?> arid;.back, took exactly five hours, 'how..far is, it between the two places! If Jaek?s age be added, to twice JaTne's''the~total would be.fortyfour years, but if the age-of Janies be; added..to.twice-. Jack's the.total, would bo only . forty years.' How .old are they respectively? And can, the .reader say offhand', and -before, making a cal- j culatipa, who, is : the older? •,". . ■ -AN ALPHABETICAL-SUM. .. A.porrespon.dept, ,"Kex,'' states that a recent alphabetical -suni took him some hours to solve,' which he did empirically, and asks whether there is any other method by which it can be done.' Most certainly there is, namely, by deductive reasoning, and the' Object of this- class of- problem is that this method alone should be adopted. -. Here is an; example :tbat permits of the sum -being- constructed very simply in that way which will be- fully explained with the. solution, nest week, and in the meantime the reader may try to reason it out logically. It -is a 1 long division sum, G.F. being the .divisor, E.D.C.C.F. the dividend, and- F.B.F.' the quotient, with no remainder. The three ■ multiplied lines are respectively, E.C.F., K.E.H., and E.C.F., while the results of the two subtractions in which there are remainders are:—X.X. with C. brought down, and E.C. with the final dividend letter F brought down. ■ LAST WEEK'S SOLUTIONS. .. ', A Bank's Gift to Charity. The Mayor had £-1800 which was divided equally by nine. Hidden Word No. 3. The hidden word is "Unimproved." and tho three clues, "Bipe", "Dump", and "Oven". The Clowns' Argument. The length of the red-painted part of the pole from "D" to "C" is ten feet, and the bar "CD" fifty-three feet. A City Block.. The, frontago is exactly one-fourth the length of the depth, namely, thirtythree feet," the block being sold on that measurement at £140 per foot. Church Hymn-board. The smallest number of plates that would be necessary is 81 (eighty-one), but if an inverted " six" be- not allowed to be used as a "nine'V 86 (eighty-six) plates would be the mmii lm numben