upper stories are let for $450 a year, the annual expense for repairs, is $36,89 cts. What per cent. does the house pay? *The rent is $875, and 875--36,89-$838,11 cts.

Then, if $12894: $838,11::$100: $6,50 per cent., Ans.

6. A bought flour for cash, and sold it to B at an advance. B sold it to C at 10 per cent., advance, and C sold it to D at $71,28 cts. advance, equal to 12 per cent. profit, which was 4 per cent. more than A made, though he bought it at $5 per barrel. Required, B's gain, how much C received, and the number of barrels in the lot?

* Since C gained 12 per cent., which was 4 per cent. more than A made, it shows that A gained 8 per cent., and sold it to B at $5,40 cts. per barrel, and B sold it to C at 10 per cent. profit; hence C paid $5,94 cts. per barrel. Then, if $1,:12 cts.::$5,94 cts.: $0,7128, C's gain per barrel, on selling it to D. And, if $0,7128:1 bbl.::$71,28 cts.: 100 bbls., Ans. 3. And since it cost C $5,94 cts., and he gained $0,7128, it stood D $6,6528 per barrel; and $665,28 cts. per 100 barrels, Ans. 2. And since it stood B $5,40 cts., and C $5,94 cts. per barrel, say 5,94-5,40-54 cts., B gained per barrel; hence, $54 per hund. bbls., Ans. 1.

CLASS II.

Required to know how an article must be sold to gain or lose so much per cent.

EXAMPLES.

1. Bought a pipe of wine, containing 126 gallons, at 10s. per gallon, but, by accident, 16 gallons leaked out. At what rate must the remainder be sold per gallon, to gain on the whole prime cost, at the rate of 12 per cent?

* First, 126 gallons, worth $210, and 126-16-110 gallons not leaked out; then, if 100:112,5::210: $236,25 cts., what it must sell for, and 236,25÷110=$2,14 cts. 7m. per gallon, Ans.

2. B imported 10 tons of iron, at $95 per ton, sundry expenses were $170. At what rate per lb. must he sell it to gain 20 per cent.?

* Cost and expense, $1120, and 10 T. 22400 lbs.

Then, if 100:120::1120: $1344, and $1344÷22400—6 cents per pound, Ans.

3. How should fish be rated, which is now worth in Boston 15s. per quintal, so that by selling it on 9 months credit, there may be 15 per cent. gain, after allowing 5 per cent. discount for present payment?

*As 100: 100+15+6:: 15:18.15s.

Interest of 100 at 5 per cent. for 9 months, is 3.75.
Hence, as 100:3,75:: 18.15:,68025s. discount.
Then, 18.15+,68025-18.830625s., Ans.

CLASS III.

Required the cost of an article, when there is gained or lost so much per cent.

EXAMPLES.

1. A merchant receives three kinds of flour; from A he receives 20 barrels, from B 25 barrels, and from C 40 barrels. He finds that A's flour is 10 per cent. better than B's, and that B's is 20 per cent. better than C's. He sells the whole at $6 per barrel. What in justice should each man receive?

* A 20×$132=$2640 | 10 per cent. on $120-$132, 85 B 25×$120-$3000 bbls. X $6=$510, it sold for? C 40×$100-$4000

9640 $5102640: $13911, A receives.

2. A bought a house for $1575, and repaired it for D, who agreed to pay him a rent of $220 per annum, which was 12 per cent. for his money that he paid for the house and its repair. What was the cost of repairing it?

* If 12 : 100 :: 220: $1833, which less 1575-$2581, Ans. 3. A father left two sons, the one 11 and the other 16 years of age, $10000, to be divided so that each share, being put to interest at 5 per cent., might amount to equal sum's when they would be respectively 21 years of age. Required, the share of each?

* Now it is evident that the youngest son must have less than half the $10000, because his share will be at interest 10 years, and the share of the oldest only 5 years. And the amount of $1 for 10 years, at 5 per cent., is $1,50; and the

amount of $1 for 5 years, at 5 per cent., is $1,25. 1,50+1,25 is 2,75.

Then, {2,75: 10000 ::

1,50: $54546, the older's share. :: 1,25 $4545,the younger's.

}

4. A and B cleared by an adventure at sea, 45 guineas, which was 35 per cent. upon the money advanced, and with which they agreed to purchase a genteel horse and carriage, whereof they were to have the use in proportion to the sums adventured, which was found to be 11 to A, as often as 8 to B. How much did each adventure?

*Each guinea £13, and 45×13=£63. 11+8=19. And, if 35; 63: : 100; £180 adventured.

Then, if{

19: 1808: £75 15s. 91d., B adventured.
: : : 11 : £104 4s. 21gd., A

66

66

Ans.

5. A had 12 pipes of wine, which he parted with to B at 42 per cent. profit, who sold them to C for $40,60 advantage; made them over to D for $605,50, and cleared thereby 6 per cent. How much per gallon did this wine cost?

* 12 pipes=1512 gallons.

If 106: 100 :: 605,50 : $571,2264, which less $40,60 $530,6264, it cost B.

Then, if 104,5 : 100 :: 530,6264: $510,1215.
And 510,1215-1512-331119 cts., Ans.

I

6. Gowns of, and of of the other of an individual estate. Suppose this estate rents for $1556,94, being equal to 6 per cent. per annum on its value, and that he sells

of his part on such terms as to yield the purchaser 8 per cent. per annum on his payment, How much does G receive, and what share has he now in the estate? 욕

First, of, and of

12 154

34

of 14.

Then, +4, and 34-2=154, Gowns of the estate. And, if 154: 1556,94 :: 17: $171,87.

Then, if 8:100:171,87: $2148,371, G receives, Ans. 1.

7. A, on preparing for a voyage to Calcutta, purchased of G, specie dollars, to be paid in 18 months, with interest. Supposing the premium on the dollars to be 3 per cent., and that G would have 5 per cent. per annum for the use of his money to be inserted in the note, which was given for $22145. I would know the sum purchased.

* The interest of 3 per cent., at 5 per cent., for 18 months, is,225, and the interest of $100, for 18 months, at 5 per cent., is $7,50.

F

Then, if 100+7,5+3+,225: 100::22145: $20000, Ans.

8. Sold a horse for $60, and by so doing lost 20 per cent., whereas, I ought to have gained 30 per cent. What was the real value of the horse?

* If 100-20:60:100: $75.

And, if 100:130::75: $97,50 cts., Ans.

9. B owns of a ship, which cost him $3691, and sells & of his part to C, at 12 per cent. advance. Required, the share of each in the ship, the cost of C's part, and how much B's part stands him.

* If 8:3691: :3:$1384,125 of $3691.

And, if 100: 112::1384,125: $1550,22, C's part cost him. 1550,22-1384,125-166,095, and 3691-166,095 $3524,905, B's part stands him.

And.C's part is of . And B's part is § of 18.

10. A bought of a store, and soon after he paid $1230,075, for of the same, which was at 10 per cent. advance on the rate of the first purchase; and to own the whole, he bought the remainder at 25 per cent. advance on it. What did the store cost him?

* If 110: 100 :: 1230,075: $1118,25, first purchase cost of 7 shares.

And, if 7:1118,25::25: $3993,75, cost of 25 shares. Then, if 7:1118,25; :5: $798,75, first purchase cost of 5 shares.

And, if 100: 125::798,75: $998,4375, cost of 5 shares. Then, 3993,75+1230,075+998,4375-86222,2625, Ans.

CLASS IV.

Required to know what would be gained or lost per cent. by goods sold at another rate, when there is gained or lost so much per cent. by being sold at a certain rate.

EXAMPLES.

1. If by selling goods at 2s. 3d. per lb., I clear cent per cent., what do I clear per cent, by selling them at 9 guineas per cwt.?

* 2s. 3d.=27d., 9 guineas is 2268d.; 2268-112—204d. per lb., and cent per cent. is 2 cents received for every cent laid out; then, if 27:200, cent per cent.: :204: 150, and 150-100-50 per cent., Ans.

2. If by selling goods at $2 per cwt. I gain 20 per cent., what do I gain or lose per cent., by selling them at $2 per

cwt.?

* If 2,5:120::2,25:108, and 108-100-8 per cent. gain, Ans.

3. If wine, sold at $1,50 per gallon, be 15 per cent. profit, what would be the gain or loss per cent. if sold at $1,25 per gallon?

* If 115:100 :: 150: $1,301, first cost per gallon.

And 1301-125=519 cts., loss on its cost at the other rate. Then, if 13049:518::100: $4,163, loss per cent., Ans.

4. Bought 126 gallons of rum, for $110. How much water must be added to reduce the first cost to 75 cts. per gallon? * If 75 cts. buy 1 gallon, how many gallons will $110 buy? From this result, subtract the 126 gallons, and you have 20 gallons, the answer.

5. Bought 115 gallons of wine, at $1,10 per gallon. How many gallons of water must be added, so as to gain $5 by selling it at $1 per gallon?

* 115×110, its cost, which plus $5-$131.

Then, as $1:1 gal.::$1314: 131 gallons of the mixture; and 131-115-16 gallons of water, Ans.

6. A merchant bought goods to the amount of $3472, which he sold at a loss of 12 per cent., and invested the proceeds of the sale in other goods, which he sold at 13 per cent. profit. Did he gain or lose by these transactions, and how much per cent.?

* 100:100-12,5:: 3472: $3038 left.

And, if 100:113;:3038: $3432,94, and 3472-3432,94 =$39,06, loss, and consequently, 1 per cent., Ans.

II. PARTNERSHIP.

EXAMPLES.

1. A clears $13 in 6 months, B $18 in 5 m., and C $23 in 9 m., his stock being $72. What then is the general stock?