Ex.2. Three persons, A, B, C, freighted a ship with 340 tuns of wine; of which, A loaded 110 tuns, B 97, and c the rest : in a storm the seamen were obliged to throw overboard 85 tuns; how much must each person sustain of the loss ? Here 110 + 97 = 207 tuns, loaded by A and B; 1 :: 110 : 27 tuns = A's loss; 97 : 24 tuns = B's loss; also as 4 : 1 :: 133 : 33% tuns = c's loss; Sum 85 tuns, the proof. or as and as 1 :: F G 3. Two merchants, c and D, made a stock of 1201; of which c contributed 75), and D the rest : by trading they gained 301; what must each have of it? Ans. c 181 15s, and D 111 5s. 4. Three merchants, E, F, G, make a stock of 700), of which e contributed 1231, 358), and G the rest : by trading they gain 1251 10s; what must each have of it? Ans. E must have 221 1s Od 2359. 64 3 8 0}}. 39 5 3 175 5. A General imposing a contribution * of 7001 on four villages, to be paid in proportion to the number of inhabitants contained in each; the 1st containing 250, the 2d 350, the 3d 400, and the 4th 500 persons; what part must each village pay? Ans. the 1st to pay 1161 13s 4d. the 2d 163 6 8 the 3d 186 13 4 the 4th 233 6 8 6. A piece of ground, consisting of 37 ac 2 ro 14 ps, is to be divided among three persons, L, M, and n, in proportion to their estates: now if L's estate be worth 5001 a year, M's 320), and n's 751; what quantity of land must each one have ? Ans. I must have 20 ac 3 ro 391*. ps. 13 1 3 O 7. A person is indebted to o 571 15s, to p 1081 3s 8d, to Q 221 10d, and to R 731; but at his decease, his effects M 304 N 23173 * Contribution is a tax paid by provinces, towns, villages, &c. to excuse them from being plundered. It is paid in provisions or in money, and sometimes in both. are are found to be worth no more than 1701 14s; how must it be divided among his creditors ? Ans, o must have 371 15s 5d 2 T04759 - 70 15 2 2.14 og Q 14 8 4 0 5302 P O T0430 4720 TOJO 3 359 R X Ex. 8. A ship, worth 9001, being entirely lost, of which belonged to s, to T, and the rest to y; what loss will each sustain, supposing 5401 of her were insured ? Ans. $ will lose 451, T 901, and v 2251, 9. Four persons, w, x, y, and z, spent among them 25s, and agree that w shall pay { of it, x }, y , and z }; that is, their shares are to be in proportion as , , , and : what are their shares ? Ans. w must pay 9s 8d 349. 6 5 34. 4 10 149. 3 10 377 10. A detachment, consisting of 5 companies, being sent into a garrison, in which the duty reqaired 76 men a day; what number of men must be furnished by each company, in proportion to their strength; the 1st consisting of 54 men, the 2d of 51 men, the 3d of 48 men, the 4th of 39, and the 5th of 36 men ? Ans. The 1st must furnish 18, the 2d 17, the 3d 16, the 4th 13, and the 5th 12 men*. Y DOUBLE FELLOWSHIP. DOUBLE FELLOWSHIP, as has been said, is concerned in cases in which th: stocks of partners are employed or continued for different times. * Questions of this nature frequently occurring in military service, General Haviland, an officer of great merit, contrived an ingenious instrument, for more expeditiously resolving them; which is distinguished by the name of the inventor, being called a Haviland. RULE, Rule*. -Multiply each person's stock by the time of its continuance; then divide the quantity, as in Single Fellowship, into shares, in proportion to these products, by saying, As the total sum of all the said products, EXAMPLES. 1. A had in company 501 for 4 months, and B had 601 for 5 months; at the end of which time they find 241 gained ; how must it be divided between them? Here 50 60 4 5 200 + 300 = 500 Then, as 500 : 24 :: 200 : 9} = 91 12s = A's share. and as 500 : 24 :: 300 : 14} = 14 8 = B's share. 2. c and d hold a piece of ground in common, for which they are to pay 541. c put in 23 horses for 27 days, and D 21 horses for 39 days; how much ought each man to pay of the rent? Ans. c must pay 23l 5s 9d. D must pay 30 14 3 3. Three persons, E, F, G, hold a pasture in common, for which they are to pay 301 per annum ; into which e put 7 oxen for 3 months, F put 9 oxen for 5 months, and G put in 4 oxen for 12 months; how much must each person pay of the rent? Ans. E must pay 5l 10$ 6d 1f-9. 11 16 10 0,45 G 12 12 7 20. 4. A ship’s company take a prize of 10001, which they agree to divide among them according to their pay and the time they have been on board: now the officers and midshipmen have been on board 6 months, and the sailors 3 months ; F as * The proof of this rule is as follows: When the times are equal, the shares of the gain or loss are evidently as the stocks, in Single Fellowship ; and when the stocks are equal, the shares are as the times; therefore, when neither are equal, the shares must Þe as their products. the the officers have 40s a month, the midshipmen 30s, and the sailors 22s a month; moreover there are 4 officers, 12 midshipmen, and 110 sailors : what will each man's share be? Ans. each officer must have 231 25 5d 0 1999 each midshipman 17 6 9 6 7 2 04. 3175 Ex. 5. H, with a capital of 10001, began trade the first of January, and, meeting with success in business, took in 1 as a partner, with a capital of 15001, on the first of March following. Three months after that they admit k as a third partner, who brought into stock 28001. After trading together till the end of the year, they find there has been gained 17761 10s; how must this be divided among the partners ? Ans. H must have 4577 9s 4d 571 16 87 747 3 114 I K 6. x, y, and z made a joint-stock for 12 months ; x at first put in 201, and 4 months after 201 more ; y put in at first 301, at the end of 3 months he put in 201 more, and 2 months after he put in 40% more ; z put in at first 601, and 5 months after he put in 101 more, 1 month after which he took out 301; during the 12 months they gained 501 ; how much of it must each have ? Ans. x must have jol 18s 6d 3419. 22 8 1 07 16 13 4 0. Y Z SIMPLE INTEREST. INTEREST is the premium or sum allowed for the loan, or forbearance of money. The money lent, or forborn, is called the Principal. And the sum of the principal and its interest, added together, is called the Amount. Interest is allowed at so much per cent. per annum ; which premium per cent. per annum, or interest of 1001 for a year, is called the rate of interest :-$o, When When interest is at 3 per cent. the rate is 3; 4 per cent. 5; 6; But, by law, interest ought not to be taken higher than at the rate of 5 per cent. Interest is of two sorts; Simple and Compound. Simple Interest is that which is allowed for the principal lent or forborn only, for the whole time of forbearance. As the interest of any suni, for any time, is directly proportional to the principal sum, and also to the time of continuance; hence arises the following general rule of calcula. tion. As 1001 is to the rate of interest, so is any given principal to its interest for one year. And again, As 1 year is to any given time, so is the interest for a year, just found, to the interest of the given sum for that time. OTHERWISE. Take the interest of 1 pound for a year, which multiply by the given principal, and this product again by the time of loan or forbearance, in years and parts, for the interest of the proposed sum for that time. Note, When there are certain parts of years in the time, as quarters, or months, or days: they may be worked for, either by taking the aliquot or like parts of the interest of a year, or by the Rule of Three, in the usual way. Also, to divide by 100, is done by only pointing off two figures for decimals. EXAMPLES. 1. To find the interest of 2301 10s, for 1 year, at the rate of 4 per cent. per annum. Here, As 100 : 4 :: 230l 10s : 91 4s 4 d. 4 |