Miscellaneous Problems 1. What is the square root of 225? 6. Find the fourth power of .25. 7. What is the volume of a cube whose edge is 2.03 inches? 8. What is the volume of a cube, one of whose sides is 121 square inches? 9. A can do a piece of work in 10 days, and B can do the same amount in 12 days. How long would it take both together to do the work? What part of the work can each do in one day? What part can both together do in one day? How long, then, will it take both together to do the whole work? 10. A can build a piece of fence in 15 days. B could build it in 18 days, and C in 30 days. In how many days could they build the fence if all should work together? 11. If A can do a piece of work in 8 days, and B in 12 days, what part of the work can both together do in one day? 12. What part of the work can both together do in 3 days? 13. What part would remain to be done after they had worked together upon it for 3 days? 14. If I should sell goods at an advance of 15% above the cost, and by so doing should gain $6.60, what is the cost? Stocks 1. The capital of a certain stock company is $40,000. Profits amounting to $3600 are to be distributed among the stockholders. of the stock? How much profit is there for each $100 2. What is the per cent of dividend to be declared? 3. How much will a stockholder receive who holds 25 shares of $100 each? 4. What per cent will a share of stock pay which costs $80 and which yields 4% a year reckoned upon the par value of $100? The income on $100 is $4; $4 is what per cent of $80? 5. What is the per cent of income upon a share of 5% stock whose par value is 100, purchased at 80? 6. What is the per cent of income upon a share of 5% stock whose par value is 50, purchased at 60? 7. When stock costs 647, what will be the cost of 40 shares, including the brokerage of 1% ? 40 × ($6478 }) = ? 8. What will be the cost of 40 shares of stock whose par value is $50 each, purchased at 43ğ without brokerage? 9. What will be the profit in buying 10 shares of stock whose par value is $100 each, at 88, and selling at 951, if brokerage of % is paid both in buying and selling? Cost = ($88 + $3) × 10; selling price = ($951 – $ }) × 10. 10. How much is gained in buying 30 shares of stock whose par value is 100, at 116, and selling it at 1191, paying 1% brokerage in both cases? 11. How much would be lost in buying 50 shares of stock at 117 and selling at 1101, paying brokerage in both cases? Miscellaneous Problems 1. A man began business with a capital of $5000. The first year he gained 20%, and added it to his capital. The second year he gained 16%, and added it to his capital. How much capital had he then? $5000 × × =? (Cancel.) 2. A man engaging in business year, and added it to his capital. gained 20%. He then had $6000. at first? 2 × × = $6000. gained 25% the first The second year he 3. I loaned $2000 at 5% interest. year I received both the interest and loaned the entire amount again at 6%. had I at the end of the second year? At the end of the the principal, and How much money 4. I loaned a sum of money at 10%. At the end of each year I collected the interest and added it to the principal. At the end of the second year I had $1210. How much did I loan at first? 5. What is the simple interest of $1250 for 3 yr. 5 mo. 17 da. at 41%? 6. What amount is due Dec. 15, 1899, on a note of $500, dated March 5, 1896, and bearing simple interest at 5%? 7. What is the volume of a cylinder whose diameter is 4 ft. 6 in. and length 12 ft. ? 8. Find the volume of a cone the diameter of whose base is 8 feet, and whose altitude is 14 feet. 9. Find the convex surface of a cone the diameter of whose base is 31 ft., and whose slant height is 12 ft. 10. What is the volume of a pyramid whose base is 7 ft. square, and whose altitude is 24 ft. ? Work-Energy - Momentum The amount of work or energy expended in raising one pound one foot against the force of gravity is called a foot pound. A foot pound is the unit by which mechanical force is reckoned. The momentum of a moving body depends both upon its weight and the speed with which it is moving. The momentum is found by multiplying the weight of the body in pounds by the number of feet through which it is moving per second. 1. How many foot pounds of force are necessary to raise an object weighing 25 pounds one foot? 25 pounds 3 feet? 2. How much energy is expended in raising a stone weighing 5000 lb. 20 feet? 3. What is the momentum of a body weighing 10 pounds and moving at the rate of 25 feet a second? 4. A mass of 500 pounds moves with a velocity of 20 feet per second. How many units of work are stored up in it? 5. Find the number of units of work in a 24-pound shot leaving a gun with a velocity of 1200 feet per second. 6. A ball weighing 5 pounds is rolling at the rate of 10 feet per second. How many units of momentum has it? 7. If this ball meets another coming in the opposite direction, and the second ball weighs 5 pounds, and is rolling at the rate of 5 feet per second, what will be the result? 8. A rifle bullet weighing 2 ounces leaves a gun with a velocity of 1000 feet per second. What is its momentum? 9. How fast would a cannon ball weighing 50 pounds have to move to have the same momentum as this bullet? 1. What is the bank discount of a note of $2000, due in 90 days, discounted at 4% ? 2. What will be the proceeds of a note of $640 when discounted at a bank for 60 days at 5%? 3. Reduce to smallest terms: 78%; 304; 524. 286 4. What fractional part of a year of 365 days is the time from July 1st to Oct. 14th? 5. 300 is 20% more than what number? 6. 300 is 20% less than what number? 7. If goods are sold for $4.90, at a loss of 121%, what was the cost? 8. If goods which cost $5.50 are sold for $6.00, what is the gain per cent? 9. How many cubic inches of capacity has a dipper in the form of an inverted cone, whose diameter, measured across the top, is 10 inches, and whose depth is 12 inches? 10. How many gallons does this dipper hold? |
