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?