can sail from A to B and back in 12 hours. How far apart are the two towns ? 59. I hired a laborer for 60 days, on condition that I should pay him $1.50 for every day he worked, and that he should pay me 50 cents for every day he was idle. At the expiration of the time, I owed him $74. How many days did he work ? 60. If Lewis earns $14 per week more than Herbert, and both together do a job of work in 8 weeks for $94, how ought the money to be divided between them? 61. By one pipe 4 gallons per hour will run into a cistern capable of holding 100 gallons, and by another pipe 3 gallons per hour will run out of it. If the first pipe is opened for one minute and then closed, and the second one opened for one minute, and so alternately, each pipe being left open for a minute at a time, in how many minutes will the cistern be filled ? 62. Twice one number equals 3 times another number, and the sum of the numbers is 1000. What are the numbers ? 63. By what number must 7 be multiplied to obtain a result 23 81 equal to the quotient of di of 55 43 64. Jan. 1, 1858, I bought on speculation a lot of fancy goods for $500 cash. May 1, 1858, I sold the goods, receiving in payment the following note, which I immediately collected. $1000. Providence, Sept. 29, 1856. For value received, I promise to pay Alfred Tyler or order one thousand dollars, on demand, with interest. James Perrin. On this pote were the following indorsements : Feb. 3, 1857, received one hundred dollars. June 10, 1857, received two hundred dollars. Nov. 5, 1857, received ten dollars. Jan. 1, 1858, received thirty dollars. March 5, 1858, received two hundred dollars. Allowing that money was worth 6 per cent per year, did I gain or lose by the speculation, and how much? 65. I bought a lot of cloth for $1000 cash, and sold it at an advance of 25 per cent, on a credit of 6 months, without grace. It turned out that 10 per cent of my sales were bad debts, and that it cost 4 per cent of the remainder to collect it. What was my net gain? 66. A person bought 25 sheep, agreeing to pay 1 cent for the first, 2 cents for the second, 4 cents for the third, and so on, paying for each sheep twice as much as for the preceding one. How much did the whole cost him? 67. How many feet long is the side of the largest square which can be made in a circle 20 ft. in diameter ? 68. When coffee was worth only as much per pound as tea, a person bought 48 pounds of coffee and 36 pounds of tea for $17.25. What was the price of each per pound? 69. A and B trade in company. A put in f of the capital and B put in the remainder. A was to manage the business, for which he was to have a salary of $800 per year; and it was agreed that, after paying this salary, the profits or losses should be shared in proportion to the capital stock of the partners. Under this arrangement, B’s share of the profits for the first year was 1f times as much as A's share of the profits added to his salary. Moreover, A's share of the profits added to his salary equalled ļ of his share of the original stock. What was each partner's share of the profits ? What was the original stock of each ? 70. A merchant invested $1000 more than ļof his capital in trade, $1000 more than į of the remainder in real estate, $1000 more than į of the remainder in bank stock, $1000 more than of this remainder in railroad stock, and the rest, $1000, in insurance stock. What was his capital ? 71. A retail dealer bought a lot of molasses at the rate of $36.10 per hundred gallons. Ile calculates that 5 per cent of it will waste in measuring; that 12 per cent of it will be bad debts; and that it will cost 5 per cent of the remainder to collect it; and he wishes to sell it for such a price that, after allowing for all these losses, he may gain 10 per cent of his original investment. For how much per gallon must he sell the molasses ? 72. A and B have annual incomes. A saves } of his each year, and B saves } of his. At the end of 4 years A has saved $1000 more than į as much as B has saved. What are their incomes ? 73. A and B hired a pasture together for $64. A pastured 3 horses for 5 weeks and 7 cows for 14 weeks. B pastured 2 horses for 6 weeks, 1 cow for 7 weeks, and 5 cows for 12 weeks. Now, if it is worth 13 times as much per week to pasture a horse as it is to pasture a cow, how many dollars ought each to pay? 74. What number is that the square root of which is 36 less than the square root of 4 times the number? 75. By selling a lot of land for as many dollars per acre as there are acres in the field, I gain 25 per cent of its cost. If I had sold it for $2250 less than I did, I should have sold it for 25 per cent less than cost. How many acres did the lot contain, and how much per acre did I give for it? 76. A certain square garden measures 500 feet on a side, and the owner wishes to lay out a walk completely around it, which shall occupy just it of the area of the garden. How wide ought the walk to be ? 77. Jan. 1, 1858, I bought a lot of shoes for $5000 cash, and immediately shipped them to New Orleans, paying 2 per cent premium for insurance and $1 for the policy. My agent in New Orleans sold them, Feb. 15, at an advance of 50 per cent on their original cost, charging 3 per cent commission for his services. He paid out $100 for freight and other expenses, and invested the sum due me, after deducting a commission of 14 per cent on the purchase, in cotton. He shipped the cotton to me in Boston, where I sold it, May 1, at an advance of 25 per cent on the sum which my agent paid for it, receiving in payment a note on 3 months. May 1, I paid $1000 in cash for freight, insurance, etc. May 3, I had the note received for the cotton discounted at a bank, and immediately invested į the proceeds in railroad stock at a discount of 15 per cent, and the other half in railroad stock at a discount of 30 per cent. July 1, a dividend of 4 per cent was declared on the stock of the first railroad. This dividend I received July 3. Sept. 1, I sold the first lot of stock at 5 per cent above par, and th4 second at 40 per cent below par. Money being worth 6 per cent, what was my gain by these transactions ? 78. If I sell a lot of goods at an advance of 25 per cent, and 25 per cent of the sales turn out to be bad debts, shall I gain or lose, and how many per cent? 79. If, by selling a lot of goods for $556.10, I shall gain 10 per cent, how many dollars shall I gain or lose by selling of the lot for $200, and the other half at an advance of 25 per cent on their cost? 80. A trader calculates that he can sell $20000 dollars worth of goods per year. He estimates that his expenses will be $800 for clerk-hire, $1000 for rent and other store expenses, $250 for transportation of goods, $600 for interest, and $100 for other expenses. At what per cent advance on the cost of his goods must be sell them to make a net gain of $2000 per year? 81. Albert can run 3 rods in 4 seconds, and Charles can run 4 rods in 5 seconds. How many seconds will it take Charles to overtake Albert if Albert bas 10 seconds the start? 82. If the base of a right-angled triangle which contains 18769 sq. ft. is twice its altitude, what is its hypothenuse ? 83. The square root of a certain number subtracted from that number, leaves a remainder equal to 16 times the square root of the number. What is the number? 1 84. The difference between the cube root of a number and the number itself is 120 times the cube root of the number. What is the number? 85. A and B traded in company. A put in 1} times as much money as B. Moreover, the money which A put in was $600 more than of the whole stock. They gained 25 per cent of their investment. What was each man's share of the gain? 86. Whitney & Dean bought a square lot of land, measuring 350 feet on a side, at 2 cents per square foot. They cut two roads, each 50 ft. wide, through the middle of it, at right angles to each other and to the sides of the field. At how much per square foot must they sell the rest to make a gain of 150 per cent on their original investment, allowing nothing for interest or expenses ? 87. I gave my note on 3 months at a bank for such an amount that I realised $4500 on it, and invested the proceeds in flour at $6 per barrel. After incurring expenses on the flour to the amount of 10 cents per barrel, I sold it at an advance of 20 per cent on its first cost; and, after paying the above-named expenses, invested the remainder in cloth at 50 cents per yard. This cloth became so much damaged by a fire, that I was obliged to sell it for ļ what it cost me. I paid $50 for expenses on account of the cloth, and invested the remainder in silks at $1.25 per yard. The very day my note at the bank became due, I sold the silks for cash at an advance of 50 per cent on their cost. Did they bring more or less than the amount of the note due at the bank, and how much ? 88. I bought a lot of goods for $250 cash, and at the expiration of 6 months I sold them at an advance of 10 per cent, receiving in payment a note on 60 days. This I immediately got discounted at a bank. What was my real gain, money being worth 6 per cent? 89. If a cubic foot of water weighs 62} pounds, how many pounds of water will a cylindrical vessel hold, if the inside diameter of its base is 3 ft. and its inside altitude is 6 ft. ? 90. A speculator purchased a lot of land. At the end of the first year, its value had increased 25 per cent. At the end of the second year, its value was 30 per cent more than at the end of the first. At the end of the third year, he sold it for 10 per cent less than its value at the end of the second year, receiving in payment a note on 4 months. This note he got discounted at a bank, receiving $9795 on it. Money being worth 6 per cent compound interest, what was his profit on the land ? 91. The hour and minute hands of a watch are together at 12 o'clock. When are they next together? 92. At what time between 3 and 4 are the hour and minute hands of a watch together? 93. At what time between 6 o'clock and 7 do the hour and minute bands of a watch make equal angles with the 6 o'clock mark? 94. At what time between 12 o'clock and 1 does the minute hand lack as much of being at the 12 mark as the hour hand is beyond it ? |