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?