First, 320+340=6607. C and D put in; then from 824/, take 660l. remains 1644. E's stock; and 824+70=894/. their whole gain; then, £. s. d. Rem. £. £. As 824 894 :: £. E. 3. Some time ago, as people fay, d. 347 3 8 72 C's 894 o d. 80 60 The remainders in the above operations being 192, 144, 24, and 96, which added together, thus, 192+144+24+96=456, which, divided by by the fum of their money, paid the quotient = 2, which is added to the farthings for the proof, thus: Note. The late Mr. Sadler has expeditiously folved this queftion by vulgar fractions; but to fhew my readers that questions of this kind are very well adapted to this rule, was the reafon of my inserting it in this place, E. 4. Four merchants, A, B, C, and D, join their ftocks and trade together, of which A put in one-half, B one-third, C one-fourth, and D one-fifth; but at the expiration of twelve months, they had the misfortune to lose 120/. what must each perfon fuffer of the faid lofs? Note. You may fuppofe any fum at pleasure to be their ftock; as, fuppofe 600l. 300 A's Sof 600l.: 200 B's ftock £. £. s. d. Rem. 9 A's 3 4 6 B's 150 23 7 64 43 C's 14019 D's Lofs E. 5. Four merchants, A, B, C, D, gain 2000l. by trade, whereof of A's fhare is equal to of B's, of C's, and of D's; what share had each? Take any number at pleasure, and divide in proportion to their shares, thus: A and B venturing equal fums of money, clear by joint trade. 3081,-By agreement, A was to have 8 per cent. because he spent time in execution of the project, and B was to have only 5; the question is, what was allotted A for his trouble? 8 Is when each fufce made of the time of continuance, as well when each perfon's ftock continues unequal time in company; fo a as of the ftock. RULE. Multiply the particular stocks of each perfon by the time of continuance, and the fum of the feveral products, make the first term in the fingle rule of three direct; the whole gain or lofs the fecond, and every man's particular stock, multiplied by its time, the third. PROOF. Add all the parts of the gain or lofs together, which must be equal to the whole. EXAMPLE I. Two perfons, A and B, enter into partnership thus ; A puts in 40%. for 18 months, and B 40/. for 12 months; they gain 120%, what is each man's share of the gain? A's Stock multiplied into his 4 months, E. 2. Three merchants, A, B, and C, enter into partnership; A puts in 657. for 8 months; B 781. for 12 months; and C 841. for and 90l. for 2 months; they gain 1667. 125. what is each man's fhare of the gain? 65. X 84 Add {90 XXXX 8 = 520 12 = A's 180 } C's 1972 Sum As S. As 1972 E. 2. Two merchants together make up a flock of 600l. A's stock continued in company 9 months, and B's 11; they gain 2007, which they divide equally; how much did each put in ? Firft, fince the gains are equal, A's stock multiplied by his time 9, is equal to B's ftock multiplied by his time 11, .. A's ftock is to B's ftock as 11 to 9. E. 4. A fhip's company take a prize, value 4000l. which they agree to divide amongst them according to their pay and time, they have been on board; now the officers and midshipmen have been on board 4 months, and the failors 3; the officers have 50s. a month, the midshipmen 40s. and the failors 28s.-moreover, there are 4 officers, 8 midshipmen, and 120 failors; I defire to know what each perfon's fhare is of the faid prize? First 4 X 4 X 50 = 800 Officers pay and time 8 X 4 X 40 = 1280 Midshipmen's ditto 120 X X 10080 Sailor's ditto 28 = Note. The above being the fhare of each company, each perfon's fhare is found as follows, thus: £. So d. Number £. 263 3 12 421 I 02/2 3315 15 9 S. d. 4 65 15 9 Each perfon's fhare The fractions, or remainders, are omitted, as inconfiderable. E. 5. A and B paid equally for a horfe, February 7, 1781; A on the 10th took him a journey into the Weft, and returned on the 10th of June following; B on the 2d of August took him into Scotland, and stayed till November 13, and this concluded his service for this year. From January 17 following A ufed him 10 Days, and in fix weeks after his return, employed him till April 30th; B then rode him from May-day to Midfummer; A had him from the 14th of July to 14 days after St. James's tide; B, on September 30th, took him into Norfolk, and came back October 19th; he then was fold for 77. 105. and they would have the money parted equitably between them, viz. in proportion to the ufe each made of their steed? = 122 First, from February 10, to June 10 September 30, to October 19 20 Days 61 208 A's time 55 179 B's time 387 the time 'S the exchanging wares for wares, or one commodity for another; and fuftain lofs or difadvantage by fuch a barter or exchange. If the commodities exchanged are not of equal value, the defect is fupplied with money. RULE. 1. Find the value of that commodity, whofe quantity is given; then find what quantity of the other, at the given rate, you can have for the aforefaid value, which quantity will be the anfwer. 2. When one has goods at a certain price ready money, but in bar. terage advances it to fomething more, fay, as the ready money price of the one is to its bartering price, fo is the ready money price of the other, to its bartering price; then the quantity of the latter commodity may be found either from the ready money or bartering price. EXAMPLE I. How much fugar, at 17. 10s. per hundred weight must be given in barter for 4 hundred weight of tea, at 125. per pound? Crt. 4 112 448 lb. at 125. per lb. 12 5376s. The value of the tea S. Crut. I :: 30)53716 C.179-6 Rem. 112 310)6712 S. 5376 |