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14. After making three of the seven equal annual payments of the face of a mortgage, I find $5850 to be still unpaid. How many dollars of principal have been paid ?
15. After the salary of a book-keeper had been increased 10%, and afterwards 8%, he received $1242 a year. What was his salary at first ?
16. By the United States Census of 1880 the total capital invested in manufactures in the State of Pennsylvania was $190055904, while the amount invested in Alabama was $9098181; Arkansas, $1316610; Delaware, $5452887; Florida, $1874125; Georgia, $10890875; Louisiana, $7151172; Mississippi, $4384492; North Carolina, $9693703; South Carolina, $6931756; Texas, $3272450. What per cent. greater was the manufacturing capital invested in Pennsylvania than in the group of the ten other States named ?
17. From an estate the widow received $9250, which was one-third; the remainder 'was divided among three children, aged respectively 15, 12, and 10 years, and they shared in proportion to their age. What per cent. of the estate did each of the children receive ?
A herder was asked how many cattle he had, and replied: “My herd increased last year 40%; should it increase at the same rate during this year and next, and I then buy 4 head more, I shall have double my present number.” How many head of cattle had he ?
19. What per cent. of the amount, at 10%, is 10% of the base ?
20. From a farm containing 180 A. 120 sq. rd., one-half was sold at one time, and one-half of the remainder at another time. What per cent. of the whole then remained?
21. A man drew 15% of his deposit from a bank, and with it paid a debt of $1119.60. What balance was left in the bank ?
22. 15% of of a number is what per cent of of it?
23. A man sold two farms for $7500 each; for one he received 25% more than it cost, and for the other 25% less than it cost. Did he gain or lose by the sale, and how much ?
24. What number is that which, being increased by 35% and 46% of itself and 76 more, will be doubled ?
25. A ranchman, when asked how many sheep he had, replied: “If my flock increases next year 20%, the next 25%, and the third year 40%, I can then sell 300, and have left double my present number. How many had he ?
26. The total number of Popes up to 1888 has been 253, of whom 197 have been Italians. What per cent. of all have been of that nationality ?
27. By widening a roadway 5%, it was made 101 yd. wide. What was its original width ?
28. Oct. 11, 1888, A bought an engine and mill for $5250, on six months credit, or 5% off if paid within 90 days, or 73% off if paid within 30 days. What amount was required for full settlement Nov. 17, 1888 ?
29. In settling an estate, an executor found 74% of it to be invested in telegraph stock, 15% in railroad stock, 37% in city bonds, $16750 in real estate, and $7350 cash in bank. Find the total value of the estate.
30. A farm is composed of 20% more grazing than grain land, and the timber is one-half of the arca. How many acres of cach, if, after deducting 12 acres for lawn and garden, there is left of the farm 1860 acres ?
31. A has 20% less money than B, and B has 25% more than C. How much has C, if A has $192 ?
32. A and B were heirs of an estate of $120000, A receiving 15% of the whole more than B. For four years thereafter the property of each increased at an average rate of 9% per annum. How much had cach at the end of that time ?
33. A man owning 62% of a factory, sold 7% of his share for $1050. At that rate, what was the value of the factory?
34. What is the per cent. of difference between 163% of 1 of a number, and 25% of } of the same number ?
35. From a cheese factory, 33630 boxes of cheese were sold in four years; the sales of the second year having been 30% greater than those for the first year, those of the third 30% less than those of the second, and those of the fourth 40% greater than those of the third. What were the sales of each year ?
36. In preparing a prize mixture for seeding pastures, Sibley & Co. mixed equal parts of clover seed and timothy with 33% as much orchard grass as clover, and 33% as much red top as orchard grass. How many pounds of each, in a consignment of 1100 pounds of the mixture ?
37. Three railroad companies carry six carloads of freight, each weighing 20 T. 6 cwt , a distance of 450 miles; the distance over the first line was 100 miles, and that over the second 125 miles. If the total charge was 15¢ per 100 pounds, how much money should each company be paid ?
38. A young man who received $21000 from his father, had, at the end of five years, only $3500 left. What average per cent. of his inheritance did he lose yearly?
39. My grocery sales increased 20% the second year, 25% more the third year, and 40% still more the fourth year; during which four years I sold $131250 worth of goods. What was the amount of my sales the first year
? 40. A father located his son upon a farm, expending for the farm, stock, utensils, and household furniture, $19512.50, the stock cost twice as much as the household furniture, which cost 75% more than the farm utensils, and the cost of the farm was 140% of the cost of the stock. How much was invested in each?
41. The general freight agent of a railroad, when questioned as to the amount of freight carried by his line, replied . “For the past four years our yearly increase over previous business has been 25%; should this be shown for the coming four years, the amount of freight then carried will be 22070 T. 625 lb. more than double the amount carried this year.” What was the number of tons carried four years ago ?
42. A last will and testament provided that three-eighths of the estate distributed should go to the widow, and the remainder be so divided among two sons and a daughter that the elder son should receive 10% more than the younger, who should receive 25% more than the daughter. What amount was received by each, the estate being valued at $58000?
PROFIT AND LOSS.
549. Profit and Loss treats of gains or losses in business transactions.
550. If, after deducting all expenses of sale, the net price is greater than the cost, the excess is a Profit or Gain.
551. If the net price received from the sale is less than full cost, the difference is a Loss.
552. The Gross or Full Cost of an article is its first cost, increased by all outlays incident to its purchase and holding to date of sale.
553. The Net Selling Price is the gross selling price, less all charges incident to its sale.
554. In ascertaining profit or loss, operations are usually performed by the rules of Percentage heretofore explained; but when the rate is a simple, common, fractional part of 100, it is more convenient to use the equivalent fraction than the decimal per cent.
555. Comparing the elements of Profit and Loss with those of Percentage, the Cost corresponds to the Base; the Per Cent. of Gain or Loss to the Rate; the whole Gain or Loss to the Percentage; the Selling Price, if at a gain, to the Amount; the Selling Price, if at a loss, to the Difference.
REMARKS —For table of ALIQUOT PARTS, convenient for use as common fractional equivalents, refer to page 89.
556. To find the Profit or Loss, the Cost and Rate being given.
EXAMPLE. —An agent paid $95 for a reaper, and sold it at a profit of 18%. What was his gain ?
EXPLANATION.-Since the agent gained 18 per cent. or 18 cents on .18 = % of gain. 1 dollar, on the $95 of cost he would gain 95 times $.18, or $17.10. $17.10 = gain.
Rule.-Multiply the Cost by the Rate.
Formula.-Profit or Loss = Cost X Rate.
EXAMPLES FOR MENTAL PRACTICE.
557. 1. A set of furniture, costing $60, was sold at 15% profit. How much was gained?
2. If I pay $400 for a piano, and gain 12% by its sale, how much is my profit?
3. Having paid $7500 for a house, I sell it at 10% advance on cost. How much do I gain?
4. After using a carriage which cost me $250, I was obliged to sell it for 20% less than it cost. What was my loss?
5. How much loss do I sustain by selling a $200 watch at 16% less than cost?
6. After paying $1200 for a lot, I built thereon a house costing $2800, and by selling both lost 8% of my investment. How many dollars did I lose?
n. One of a road team cost $400 and the other $500. How much is lost, if the team is sold at 25% below cost?
8. I invested $10500 in Southern lands. If 20% of the land proved to have a worthless title, how many dollars were lost?
9. Since paying $14000 for a stock of teas, the price has advanced 5%. How much has the stock increased in value ?
EXAMPLES FOR WRITTEN PRACTICE.
558. 1. Three houses, bought for $5000, $6500, and $8250 respectively, were sold so that a gain of 12% was realized on the first, and 7% on the second, while the third was sold at 6% below cost. Find the net gain or loss?
2. A stock of goods costing $15600 was sold at a loss of 12%, and 15% of the selling price was in bad debts. What was the total loss sustained ?
3. A canal boat, loaded with 8400 bushels of wheat, collided with a bridge pier and sprung a leak, by which 21% of the cargo sustained a damage equal to
of its value. What was the loss sustained, the wheat having been invoiced at 754 per bushel?
4. A peddler paid $46.50 for butter, $17.60 for eggs, and $36 for dried berries. He sold the butter at a profit of 103%, the eggs at a profit of 20%, and lost 5% on the berries. What was his net gain?
5. Having paid $1640 for a box of furs, and $18.50 expressage on the same, I sold 25% of the stock at a gain of 35%, 15% at a gain of 20%, 30% at a loss of 2%, and the remainder at cost. How much did I gain or lose?
6. An agent bought three reapers, paying respectively $90, $120, and $150. He sold the first at 10% loss, the second at cost, and the third at 10% gain. What was his profit by the transaction?
7. A contractor bought 52 M bricks at $5.60 per M, and sold of them for of their cost, and for the remainder received $150. What amount did he lose ?
8. A grocer bought 7 barrels of sugar, each weighing 315 pounds, at 6}¢ per pound, and sold it so as to gain 163%. Find the amount of his gain.
9. How much is gained by purchasing 3 carloads of corn, of 750 bushels each, at 624 per bushel, and selling 40% of it at a gain of 121%, and the remainder at a gain of 7%?
559. To find the Cost, the Gain or Loss and the Rate of Gain or Loss being given.
EXAMPLE.-An agent gained $17.10 by selling a reaper at 18% profit. What must he have paid for it? OPERATION.
Since the agent's whole gain was $17.10 and since his
gain on 1 dollar of cost was 18% or 18 cents, the cost must 18% = .18) 17.10
have been as many times 1 dollar as $.18 is contained times $95 = cost.
in $17.10, or $95.
Rule.- Divide the gain or loss by the per cent. of gain or loss.
Formula.—Cost = Gain or Loss – Rate.
EXAMPLES FOR MENTAL PRACTICE.
560. 1. What was the cost, if I lost $15 by selling a machine 15% below cost?
2. By selling a farm at a gain of 10%, I realized a profit of $350. Find the cost of the farm.
3. A yacht was sold for $1250 less than cost, its owner thereby losing 12% of the cost. What was the price paid?
4. By selling a consignment of silk for 11% above the invoice price, a gain of $484 was realized. Find the invoice price.
5. A suit of clothes, becoming damaged, was sold at a loss of 13%, whereby the tailor lost $5.20. How much did the suit cost when made?
6. What must have been the cost of a necklace, if its owner, by selling it at a loss of 15%, received $45 less than it cost?
7. By selling a coach for $63 above cost, I gained 7% on my purchase price. How much did it cost?
8. Having received $105 more for a house than its cost, I find my profit to be 10% How much did I pay for the house?
9. A book-seller lost 65¢ on an album, and thereby sustained a loss of 65%. Find the cost.
EXAMPLES FOR WRITTEN PRACTICE.
561. 1. What must have been the cost of a watch and chain, if $6.90 was lost by selling them at 12% below cost?
A dealer sold a piano at 25% profit, and with the proceeds bought another which he sold at 20% profit, realizing a total gain of $250. What was the cost of each?
3. By selling a lot for $1680, I received 40% more than twice its cost. At what price did I purchase it?
4. A sells a horse to B and gains 15%. If B paid 25% of $420 more for the horse than A did, at what price did A buy it?
5. Having bought a house of A at 12% less than it cost him, I added $430 in repairs, and sold it for $7293, thereby gaining 10% on my investment. How much did the house cost A?
6. A miller's gain in business for four years aggregates 37% of his capital. If his gain is $3000, and he withdraws his gain and capital and invests it in a farm, at $55 per acre, how many acres can he buy?
7. A merchant bought goods and paid freight on them equal to 12% of their first cost; he then sold them at 61% profit on the full cost, receiving 60% of the price in cash and a note for $1309, the amount unpaid. What was the first cost of the goods?
8. A peddler sold 25% of a purchase of butter at 16% profit, and the remainder at 161% profit. What was the cost, if the total gain was $39.60?
9. A dealer sold 35% of a purchase of leather at 14% profit, and the remainder at 5% loss. If his net gain was $87.50, what must have been the cost?