I. Questions in Vulgar or Decimal Fractions. 1. Bought 83 yards broad cloth for L.721%; what must it be fold at per yard, to gain L. 10 on the whole? 2. Divide a guinea among four men, A, B, C, and D, in the proportion of,,, and refpectively; how much will each draw? 3. How many square feet are contained in a floor whofe length is 23 feet 10 inches, and breadth 18 feet 6 inches? 4. Purchased a fhip for L.185og, at what fhould of be charged, to gain 250 guineas upon the whole? 5. The dimensions of a block marble are 5 feet 11 inches, 4 feet 2 inches, and 3 feet 4 inches; what is its folidity? 6. Bought a pair of filver buckles, wg. 4 oz. 8 dwt. at 4s. 9d. per oz. and received of the price for discount; what did they coft me? 7. Required the folidity and price of a log of mahogany 164 feet long, 5 broad, and 4 feet thick, at 10 d. per folid foot? 8. What is the value of a filver tea-pot weighing 1 lb. at 7s. 6d. for 1 ounce? 9. If of a yard, ell English wide coft 16s. 8d.; what will 15 yards 7 yard wide, cost of the fame fineness? 10. How many deals, 12 feet 8 inches by 9 inches broad, will be required for a floor 361 feet by 24, allowing inch in breadth for feaming? 11. A box of goods, 6 feet long, 3 broad, and 4 deep; what is the weight at 93 lb. per folid foot, and what is the freight at L.4 134 per ton, containing 40 folid feet? 12. Three men can do a piece of work, the first in 10 days, the second in 12 days, and the third in 15 days; in what time will all the three do it? 13. How many yards of paper, yard wide, will line a room 19 feet 7 inches long, 15 feet 10 inches broad, and the height from the belt to the cornice 8 feet? 14. Three partners, A, B, and C, purchase a sugar work, of which A paid r, B, and C paid L.750; what was C's fhare? what did the work coft? and what did A and B each contribute towards the purchase? 15. A, B, and C, were to fhare,, and respectively of L.15000; but C's part being loft by his death, it is required to divide the whole fum proportionably between the other two? CHAP. X. VARIETIES IN PROPORTION. Sect. I. INSURANCE. INSURANCE is a contract, whereby one party engages to pay the loffes which the other may fuftain, for a ftipulated premium, which varies according to the risk. The parties who engage to pay the damage, are called the Infurers or Underwriters; and the parties for whofe fecurity they engage, are called the Infured. POLICY is the writ fpecifying the conditions agreed upon be tween the underwriters and the infured. It is an ufual article in the policy, that in cafe of lofs, the underwriters are to be allowed a fmall discount or abatement, which is generally 2 per cent.; in this cafe the infured receives only L.98 for the L. 100, and this L.98 is called the SHORT RECOVERY. COVERING PROPERTY, or covering the Out-fet, is when the value of the cargo, with the premium and discount, are alfo infured, and although infurances for a greater fum than the infured had really at risk, be contrary to law, yet fome latitude is allowed in this refpect; for if the owner were to infure no more than the exact value of his property, he would lose the premium of infurance, and the abatement, if any was agreed on. ift, To find the premium, work by the rule in COMMISSION. Or, when the rate is given in guineas, we may add part to the fum before we calculate for the pounds; or we may calculate for the pounds, and add part to the answer. 20 Ex. What is the premium on L.635 at 4 guineas per cent.? 2d, To find the short recovery, fubtract the discount from L. 100. As 100 is to the remainder, fo is the fum to the fhort recovery; or work by aliquot parts. Ex. What is the fhort recovery of L.1250; difcount 2 per cent.? 100: 98: 1250: L.1225 or 1250 L.1225 fhort recovery. 3d, To find how much fhould be infured to cover any fum, fubtract the amount of the premium and difcount (if any) from L.100. As the remainder is to L. 100, fo is the value, to the fum which covers it. Ex What fum must be insured to cover L.180, premium 8 per cent. abatement 2 per cent. L.200 Proof. Sum infured is 100 8+2 10 4 4th, If a voyage be infured out and home, the premium outward must be confidered as part of the value on the homeward property, and the fum neceffary to cover it computed accordingly. Ex. To infure L. 180 out and home, at 8 per cent. each voyage, abatement 2 per cent.; compute thus: 90: 100: L.180: L.200, to be infured outward, premium on L.200 outwards at 8 per cent. is L.16. 90: 100: L.196: L.217: 15: 6 Anf.; fum to be infured home; the premium on which is L.17: 8:5; and if the ship be loft on the homeward voyage, from the fum insured home, L.217 156 4.: 7: I L.213 8:57 L.16 Covered property, L.180 The Rule is. Find by the laft cafe how much will cover the value for the voyage out, on this fum calculate the premium which add to the value on board, then find how much will cover this fum. Questions for Practice. 1. What is the premium on L.320 at 14 guineas per cent.? on L.542 at 2 guineas per cent.? 2. 3. 4. 5. on L. 1265 at 3 guineas per do.? on L. 1850 at 12 per cent.? guineas per cent.? 6. At 2 per cent. difcount, what fum will be recovered for L.2396: 10.? 7. What is the short recovery of L.1974: 13: 4 insured, when discount is allowed at 1 per cent.? 8. What fum must be insured to cover L.1305, premium 10 per cent.? 9. How much must be infured to cover L.987: 18, premium 12 guineas, abatement 2 per cent.? 10. If the premium be 8 per cent. and abatement 2 per cent.; what fum must be paid to infure L.2160 for a voyage out and 'home? 11. What will be the amount of insurance out and in, to cover L.1486:7, premium at 9 guineas discount, discount 2 per cent. in cafe of lofs, and what fum must be insured to cover the infet? 12. Infured at the fun-fire office on my tenement in the Trongate, to the value of L.1575, what fum muft I pay yearly, at 3s. 6d. per L. 100, to keep the policy in force? Sect. II. GAIN AND LOSS. ift, To find the gain or lofs per cent., on any article, when the prime coft and profit or lofs upon it is given. As the prime coft is to the profit or lofs, fo is L.100 to the rate per cent.? Ex. 1ft, Bought cotton at 3s. 4d. per lb. and fold it for 4s. what was the gain per cent.? As 40d. : 8d.:: 100: 20 per cent. 2d. Sold cloth for 9s. 7d. per yard, which coft ros. 5d. what was the lofs per cent.? 125d.: 10d. : : 106. : 8 per cent. 2d. To find the felling price, when the prime coft and rate per cent. proposed to be gained or loft is given. As L.100 is to 100 with the rate per cent. added to it in case of gain, and deducted in cafe of lofs, fo is the prime coft to the felling price. Ex. 1ft, Bought cotton at 3s. 4d.; at what muft I fell it to gain 20 per cent.? 100: 120 :: 35. 4d. 31/1 1,00)4,00 45. Answer. Ex. 2d, Loft 8 per cent. by cloth which I bought at 1os. 5s.; what did I fell it at? 100: 92:: 10s. 5d. : 9s. 7d. Anf. 3d, To find the prime coft, when the rate per cent. and selling price is given. As L.100 with the rate per cent. added or deducted is 100, fo is the felling price to the prime coft. Ex. 1ft, Sold cotton at 4s. by which I cleared 20 per cent. what did I buy it for? Ex. 2d, By felling cloth at 9s. 7d, I loft 8 per cent.; what was the prime coft? 92: 100: 9s. 7d. : 10s. 5d. Answer. 4th, To find a proportional rate on one advanced price by having another, and the rate on it given. As the price whofe rate per cent. is given, is to L.100 with the rate per cent. added or deducted, fo is the given price, to a fourth number, from which fubtract 100, in cafe of gain; but which subtract from 100, in cafe of lofs. Ex. 1ft, By felling rum at 1cs. I cleared 15 per cent.; what do I gain by felling at 12s. 6d.? Sixpences. Sixpences. 20: 115:25 4)575 5 143-100-434 per cent. Answer. |