0 2. If 7 men in 12 days can reap 84 acres, how many acres can 20 men reap in 5 days? days. men. acres. days. 12 :7: 84 : :20: : 5 7 20 men. , 00 3. If 12 men in 5 days can reap 100 acres, how many inen in 12 days can reap 84 acres ? Ans. 7 men. 4. If 20 men in 5 days can reap 100 acres, how many acres can 7 men reap in 12 days ? Ans. 84. 5. If 20 men can build a wall 100 ft. long, 6 ft. high, and 4 feet thick, in 12 days, how many men can build a wall the same length, 8 feet high, and 3 feet thick, in 6 days? days. thick. Nigh. mea. high. thick. days. 6:4:6 : 20 : ; 8:: 3 :: 12 4 8 24. 160 144 480 12 144)5760(40 Ade. 576 8. If 40 men can build a wall in 6 days, 100 feet long, 8 feet high, and 3 feet thick, how many men can build a wall the same length, 6 feet high, and 4 feet thick in 12 days ? Ans. 20ʻmen. 7. If 20 men in 12 days, of 15 hours each, can build a wall 100 feet long, 10 feet high, and 6 feet thick, how mány men can build a wall in 15 days, of 12 hours each, 200 feet long, 12 feet high, and 5 feet thick. hours. days. thick. high. long. long. high. thick. days. bours. 12:15: 6:10 : 100 20 :: 200 :: 12 :: :: 12 :: '15 10 20 men. 8. If 40 men în 15 days, of 12 hours each, can build a wall 200 feet long, 12 feet high, and 5 feet thick, how many men in 12 days, of 15 hours each, can build a wall 100 feet long; 10 feet high, and 6 feet thick ? : Ans. 20 men. 9. If 10 bushels of oats supplies 18 horses 20 days, how many bushels will serve 60 horses 36 days ?. Ans. 60 bushels. If ,98 lb. of bread will be sufficient for 7 men 14 days, how much will suffice 21 men 3 days? Ans. 631b. 1 SIMPLE INTEREST. Simple Interest is a profit allowed (or paid) for the use of money loaned, or for forbearance of payment. The allowance for £100, or 100 dolls. for one year is called the ratio, or rate per cent ; sometimes distinguished by r. The sum loaned, or that for which paymem is forborne, is called the principal ; sometimes distinguished by p. The years and parts of a year, &c, for which interest is paid, is called the time ; sometimes distinguished by t. The principal and interest added into one sum, is called the amount ; sometimes distinguished by a. Various methods have been given by authors, to find the interest of a given sum ; some of those methods are not so general, as might be wished ; for instance, multiplying the principal by half the number of months, and dividing the product by 100, will give the interest for the time when the rate is 6 per cent ; but in no other case, or at any other rate per cent. The best general rule for calculating interest (which holds good not only in finding the interest of any sum proposed, but also in calculating commissions, ensurance, discount, &c. at any rate per cent) is the following. CASE I. When the interest of any sum is required. for one year. 1. If the given privcipal is dollars. Multiply by the rate per cent, and divide by 100, which division is made by pointing off the two right hand figures ; those at the left of thie point will be dollars, those pointed off, decimals of a dollars för eents) 2. If there are cents, or cents and mills, or miles only given in the principal. Multiply by the rate as before, and if cents were viven, point off four, if mills were given, point off five places* of right hand figures; those at the left of the point (if any) are doilars; the next two places of figures are cepts, the next one mills ; if any are at the right of the mills, it is a decimal of a milli A * If there are not so many places as required; to be pointed supply them by prefixing ciphers. 7 Nore. The questions in this case may be proved by division, when dollars are given. EXAMPLES 1. What is the interest of 537 dolls. for one year, ať 6 per cent. per annum? 537 6)3222 6 537 proof. dolls. 32,22 Ans. 2. Required the interest of $ 43,21, for a year, at 5 per cent. 43,21 5 dolls. 2,16,0,5 Ans. 3. Required the interest of 93 cents for a year, at @ per cent. per annum. ,93 6 905,5,8 Ans. 5 cents, 5 mills to 4. What is the interest of 9 mills for a year, at 4 per cent? 9 1,00,0,36 Ans. ,36 of a mill, or thirty six hundredth parts of a mill. 3. If the given principal is sterling money, or any currency in pounds, shillings, pence, &c. Multiply the whole of the principal, by the rate per cent, (as in Compound Multiplication) and point off the two right hand figures in the pounds of the product, (which is dividing by 100) those at the left of the point, will be pounds interest, Reduce those two figures pointed off, to shillings, taking in or adding the figures in the shilling's place of the product if any ; then point off two figures from the right of this product, those at the left of the point will be shillings interest; then reduce the last figures pointed off to pence, taking in the pence in the product, if any, and point off as above, for pence of interest, &c. Note 1. The best method is, instead of points, to draw a line downward, so as to cut of the two right hand fig. ures of the pounds in the product; then in reducing to shillings, pence, &Co set two figures of each product on the right of this line, those at the left (if any) will be shillings, pence, &c. NOTE 2. To prove these examples, multiply the interest by 100, and divide by the rate per cert, the quotient will be equal to the principal ; if there is a remainder in the interest, add it to the product. EXAMPLES. 1. What is the interest of £936 1871, for a year, at 6 per cent. per annum ? £986 18 74 principal. 6 rate. 31:34 £936 18 7 proof. Ans. £ 56 4 34 * interest. *. 2. What is the amount of a note of £738 9 4 for a year, at 6 per cent. per annum ? Principal at 738 9 4 6 |