MISCELLANEOUS EXAMPLES. 926. 1. How many thousand shingles will cover both sides of a roof 36 ft. long, whose rafters are 18 ft. in length? 2. From of of of 70 miles, subtract .73 of 1 mi. 3 fur. 3. What number is that from which if 7 is subtracted of the remainder is 911? 4. What part of 4 is of 6? 5. What number increased by 1, 4, and of itself equals 125? 6. What is the hour, when the time past noon is equal to of the time to midnight? 7. If $240 gains $5.84 in 4 mo. 26 da., what is the rate per cent? 8. If 24 men in 189 da., working 10 h. a day, dig a trench 33 yd. long, 23 yd. deep, and 5 yd. wide, how many hours a day must 217 men work, to dig a trench 234 yd. long, 24 yd. deep, and 33 yd. wide, in 51⁄2 days? 9. What is the difference between the interest and the bank discount of $450 at 5%, for 6 yr. 10 mo. ? 10. A younger brother received $6300, which was as much as his elder brother received. How much did both receive? 11. Reduce .7, .88, 727, .91325 to their equivalent common fractions. 12. A man by selling a lot of goods for $438, loses 10%. How much should the goods have been sold for to gain 12%? 13. For what sum must a note be drawn at 4 mo., that the proceeds of it, when discounted at a bank at 7%, shall be $875.50? 14. Three persons engaged in trade with a joint capital of $2128; A's capital was in trade 5 mo., B's 8 mo., and C's 12 mo.; A's share of the gain was $228, B's $266.40, and C's $330. What was the capital of each? 15. Henry Truman purchased corn of John Bates, on 2 months' credit, as follows: Aug. 27, 300 bu. @ $.35; Aug. 31, 150 bu. @ $.40; Sept. 7, 500 bu. @ $.38; Sept. 12, 200 bu. @$.42; Sept. 25, 250 bu. @$.40. When was the account due per average? 16. A, B, and C can do a job of work in 12 da., C can do it in 24 da., and A in 34 da. In what time can B do it alone? 17. If a man travels 7 mi. the first day, and 51 mi. the last, increasing his journey 4 mi. each day, how many days will he travel, and how far? 18. What is the difference between the true and bank discount of $2500, payable in 90 days at 7% (allowing grace)? 19. I sold of a lot of lumber for what of it cost. per cent did I gain on the part sold? What 20. If $500 gains $50 in 1 yr., in what time will $960 gain $60? 21. A dealer received an invoice of crockery, 12% of which was broken. At what per cent above cost must the remainder be sold to clear 25% on the invoice? 22. The sum of two numbers is 365, and their difference is .0675. What are the numbers? 23. If the interest of $445.62 is $128.99 for 7 yr., what will be the interest of $650 for 3 yr. 10 mo. 15 da., at the same rate? 24. What sum must be invested in stocks bearing 6%, at 105, to produce an income of $1000? 25. A man exchanges 250 shares of 6% stock, at 70, for 8% stock, at 120. What difference does it make in his income? 26. A boy 14 years old is left an annuity of $250, which is deposited in a savings bank at 6%, interest payable semiannually. How much will he be worth when of age? 27. If a boy buys peaches at the rate of 5 for 2 cents, and sells them at the rate of 4 for 3 cents, how many must he buy and sell to make a profit of $4.20 ? 28. A fox 30 rd. ahead of a hound runs 19 ft. while the hound runs 20 ft. How far will the fox run before he is over taken? 29. How long is a rope from the top of a pole 50 ft. high to the top of another 20 ft. high, the poles being 16 ft. apart? 30. Three men paid $100 for a pasture; A put in 9 horses, B 12 cows for twice the time, and C some sheep for 2 times as long as B's cows; C paid one half the cost. How many sheep had he, and how much did A and B each pay, if 6 cows eat as much as 4 horses, and 10 sheep as much as 3 cows? 31. A fountain has 4 receiving pipes, A, B, C, and D; A, B, and C will fill it in 6 hours, B, C, and D in 8 hours, C, D, and A in 10 hours, and D, A, and B in 12 hours; it has also 4 discharging pipes, W, X, Y, and Z; W, X, and Y will empty it in 6 hours, X, Y, and Z in 5 hours, Y, Z, and W in 4 hours, and Z, W, and X in 3 hours. Suppose the pipes are all open and the fountain full, in what time will it be emptied? 32. Find the cost, at 18 cents a square foot, of paving a space in the form of a rhombus, if its sides are 15 ft., and a perpendicular drawn from one oblique angle will meet the opposite side 9 ft. from the adjacent angle. 33. Four boys are playing at hare and hounds, the two representing hares being 45 ft. in advance of the two representing hounds. Each hound's leap covers 6 ft. of ground, and each hare's leap 41 ft., but the hares take 4 leaps to the hounds' 3. In how many leaps will the hounds overtake the hares? 34. Five men can do a piece of work in 9 da. How soon after beginning must they be joined by two more so as to complete the work in 8 da. ? 35. Four men contracted to do a certain piece of work for $8600; the first employed 28 laborers 20 da., 10 h. a day; the second, 25 laborers 15 da., 12 h. a day; the third, 18 laborers 25 da., 11 h. a day; and the fourth, 15 laborers 24 da., 8 h. a day. How much should each contractor receive? 36. If I exchange 75 railroad bonds of $500 each, at 64, for bank stock at 105, how many shares of $100 each shall I receive? 37. A flour merchant bought 120 bbl. of flour for $660, paying $5.75 for first quality and $5 for second quality. How many barrels were first quality? 38. Two mechanics work together; for 15 days' work of the first and 8 days' work of the second they receive $61, and for 6 days' work of the first and 10 days' work of the second they receive $38. How much does each man earn? 39. A dairyman took some butter to market, for which he received $49, receiving as many cents a pound as there were pounds. How many pounds were there? 40. A mechanic received $2 a day for his labor, and paid $4 a week for his board; at the expiration of 10 weeks he had saved $72. How many days did he work, and how many was he idle? 41. To what would $250, deposited in a savings bank, amount in 10 yr., interest being allowed semiannually at 6% per annum? 42. How much water is there in a mixture of 100 gal. of wine and water, worth $1 per gal., if 100 gal. of the wine cost $120 ? 43. If a pipe 3 in. in diameter will discharge a certain quantity of water in 2 h., in what time will 3 two-inch pipes discharge 3 times the quantity? 44. William Jones & Co. become insolvent and owe $8100. Their assets amount to $4981.50. What per cent of their indebtedness can they pay, allowing the assignees 21% on the amount distributed for their services? 45. I shipped a car load of cattle to Boston, and offered them for sale at 25% advance on the cost; but the market being dull I sold for 14% less than my asking price, and gained thereby $170. How much did the cattle cost; for how much did they sell; and what was my asking price? 46. What must be the dimensions of a cubical cistern to hold 2000 gallons? 47. A vessel having sailed due south and due east on alternate days, was found, after a certain time, to be 118.794 miles southeast of the place of starting. What distance had she sailed? 48. If 34 bu. of corn are equal in value to 17 bu. wheat, 9 bu. of wheat to 591⁄2 bu. of oats, and 6 bu. of oats to 42 lb. of flour, how many bushels of corn will purchase 5 bbl. of flour? 49. If stock bought at 92 will pay 7% on the investment, at what rate should it be bought to pay 10%? 50. A merchant in New York paid $2000 for a bill of exchange of £400 to remit to Liverpool. What was the rate of exchange? 51. A, B, and C start from the same point, to travel around a lake 84 miles in circumference. A travels 7 miles, and B 21 miles a day in the same direction, and C 14 miles in an opposite direction. In how many days will they all meet? 20922 52. The exact solar year is greater than 365 days by about 28238 of a day. Find approximately how often leap year should come, or one day be added to the common year, in order to keep the calendar right. 53. What per cent shall I gain by purchasing goods on 6 mo., and selling them immediately for cash at cost, money being worth 7% ? 54. What sum must a man save annually, commencing at 21 years of age, to be worth $30000 when he is 50 years old, his savings being invested at 5% compound interest? |