28. A cubic foot of a certain grade of coal weighs 52.25 pounds. How many cubic feet of bunker space are required to stow 84.5 tons (answer to nearest tenth)? Answer, 3,622.5 cubic feet. PERCENTAGE. Per cent is Any per cent of a number is so many hundredths of it. Thus, 1 per cent of a number is of it, 2 per cent is, etc. from the Latin per centum, and means by the hundred. The sign of per cent is %, read per cent. Thus, 5% is read five per cent. In all operations with per cent it may be expressed in two ways: First, as a common fraction; second, as a decimal. Thus, the following expressions are equivalent: One per cent, 1%, is 100 or .01 3 4 100 50 or .03 Four per cent, 4%, is 125 or .04 Per cent, which is expressed as a mixed number, may be reduced to equivalent expressions by complex fractions and decimals. Thus, which may be reduced to also, 4%.045. 4 41% = 100 9 200 Common fractions may be reduced to hundredths and then read as per cent. Thus, .16% or 16%. = How many per cent are equivalent to the following fractions: Percentage embraces the various operations with per cent. In percentage three quantities are considered: (1) The base; (a) the rate; and (3) the percentage. The base is the number upon which the per cent is estimated. The rate is the per cent when expressed as a common fraction or as a decimal. The percentage is the result of taking the per cent of the base. Any two of these quantities being given, the third may be found. There are four cases. CASE I. Given the base and the rate, to find the percentage. 1. What is 25% of 32? 2. What is 7% of 162? Operation. 162 .07 11.34 Solution.-7% is .07. Multiplying 162 by .07, the result is 11.34. RULE: Multiply the base by the rate, the product will be the percentage. Whether the rate should be expressed as a common fraction or as a decimal must be a matter of judgment. That form of expression is best which is simplest or most convenient in the given example. 9. What is 81% of 33.62? Answer, 2.75684. 10. Elements are the simple substances or principles of which, according to early natural philosophers, the physical universe is composed. The number of elements known is about 80. There are 42 common elements such as gold, nickel, lead, copper, oxygen, hydrogen, etc. What % of the total number of known elements is the number of common elements? Answer, 52%. 11. There are 27 rare elements such as indium, rhodium, etc. What % of the total number discovered is the number of rare elements? Answer, 334%. 12. The elements recently discovered are radium, helium, argon, etc. What part of the total number of elements are those recently discovered? Answer, 133%. 13. The fleet consisted of 20 ships; of these 20% were in the navy yards for repairs. How many were in the navy yards? Answer, 4. 14. $320,000 was appropriated for a ship's repairs. Of this 75% was for the steam engineering department and the rest for the hull department. How much for the hull department? Answer, $80,000. 15. The total wages paid to an enlisted man for 4 years was $2,400, of this he saved 37%. How much did he save? Answer, $900. 16. A man used 177.6 pounds tin, 7.4 pounds copper, and 15 pounds antimony in a mixture for Babbitt metal. What per cent of each did he use? Answer, 88.8% tin, 3.7% copper, and 7.5% antimony. 17. In the fleet of 15,000 men, 9,375 are trained men, the rest are recruits. What % are recruits? Answer, 37%. 18. The fleet mobilizes at Provincetown with 33,000 tons of coal in the bunkers; they reach Norfolk after fleet practice with 22,000 tons expended. What % of their coal is left? Answer, 334%. 19. A ship had an engineer's force of 235 men; there were 875 men all told in the crew. What % of the whole crew was the engineer's force? Answer, 26%. 20. There were 1,564 gallons of oil in all of the oil tanks on the ship; 396 gallons of it was cylinder oil. What % was cylinder oil? Answer, 25125%. 391 21. 1,000 gallons of it was machine oil. What % was machine oil? Answer, 6337%. 22. A machinist's mate, second class, had his salary increased from $44 to $60.50 when he was rated first class. What was the % of increase? nswer, 37%. 23. The antifriction metal used in the Navy is composed f the following: 88.8% tin, 3.7% zinc, 7.5% antimony. How many of each of the above elements are contained in a bearing, the Babbitt metal of which weighed 87 pounds? Answer, 77.256 pounds tin, 3.219 zinc, 6.525 pou ds antimony. 24. The high-pressure valve of a main engine travels 4 inches when the links are run out full length. If the links are adjusted so hat the valve travel is decreased 30%, what will the valve travel be in inches? Answer, 2.8 inches. 25. The New Hampshire received 2,250 tons of coal on board during a recent coaling. 1,575 tons of it was burned during the following two weeks; what % of the amount received remained? Answer, 30%. 26. A ship received $31,000 worth of provisions. After sailing it was found that $461 worth of them was spoiled, and were surveyed. What % of the provisions were surveyed? Answer, 15%. 27. The salary of a machinist's mate, second class, is $44 per month; he allots $40 of it to his mother. What % of his wages does he allot? Answer, 9010%. 28. A piece of stock weighed 45 pounds; after being turned to a certain shape it weighed 35 pounds. What % of the stock was removed? Answer, 22%. CASE II. Given the base and percentage, to find the rate. What per cent of 8 is 2? Operation. 1=25%. Solution.-2 is of 8; is 25%. 2. What per cent of 56 is 3.5? Operation. 3.556.0625 Solution.-Dividing 3.5 by 56 the result is .0625. .0625 is 6 per cent. One per cent of 56 is .56; then 3.5 is as many per cent as .56 is contained times in 3.5. RULE: Divide the percentage by the base; the quotient will be the 11. The Vermont got under way with 1,200 tons of coal on board; she used 62% before dropping anchor. How many tons had she left? Answer, 450 tons. 12. A ship's complement was 880; she left port with 93% of them on board, the rest being stragglers. How many did she leave behind? Answer, 55. 13. A T. B. D. took 160 barrels of fuel oil and used 63% of it. How much remained on board? Answer, 149.333 barrels. 14. The Charleston's complement is 648; of these 62% are in the engineer's force. How many are there in the deck complement? Answer, 243. 15. A C. P. O.'s wages, second enlistment, are $84 per month; of this he saves 713%. How much does he save? Answer, $60. 16. Of the remainder, 16% are ship's expenses. How much has he left for liberty? Answer, $20. 17. The principal losses of energy in a boiler are due to incomplete combustion and high temperature of gases passing to waste through the smoke pipe, so that only 60% to 70% of the total energy contained in the coal is converted into useful work. There were 110 tons of coal burned in a recent 4-hour speed trial of a battleship. From a test it was found that 1 pound of the coal used contained 14,535 heat units. If 65% of the total energy stored up in the coal was converted into useful work, how many of the heat units in each pound of coal were wasted? Answer, 5,087.25. 18. After steam leaves the boiler further losses are experienced as the steam traverses the steam lines and cylinders due to radiation and in the cylinders due to incomplete expansion, the action of the cylinder walls, and principally the heat carried to waste in the condenser. The work performed from the energy supplied by the boilers does not amount to more than from 10% to 20%. If an engine developed 8,250 horsepower per minute, assuming that the losses due to the preceding causes amounted to 85%, what was the total energy in horsepower wasted per minute? Answer, 46.750 horsepower. 19. All of the work made available by the steam driving the piston does not reach the propeller, owing to losses in the mechanism, such as friction, etc. The energy wasted in this operation amounts to about 20%. Assuming that the losses from friction, etc., in the above engine amount to 18%, how much of the horsepower developed by the engine was left to drive the propellers? Answer, 6,765 horsepower. 20. Of the work done by the engine, from 50% to 60% is used in overcoming the resistance to the vessel and driving her ahead. Owing to the losses in friction and the edgewise resistance of the water on the edges of the blades, these augment the resistance and the slip. Assuming that the losses of the ship due to the above causes amount to 55%, how much of the energy developed by the engine was left to drive the ship? Answer, 3,044 horsepower. CASE III. Given the rate and percentage, to find the base. 1. 15 is 25% of what number? Solution.-25% is . Since 15 is of some number, the number is 4×15, or 60. 2. 4.93 is 17% of what number? 17% = .17. 4.93.17 = 29. Solution.-17% is .17. Since some number multiplied by .17 gives the product of 4.93, the number is 4.93 divided by .17, or 29. RULE: Divide the percentage by the rate. The quotient will be the base. 3. 60 is 20% of what number? Answer, 300. 9. 45 is 1% of what number? Answer, 3,000. 10. 2.25 is 12% of what number? Answer, 18. 11. The fleet has steamed 1,100 miles, which is 33% of the journey. What is the length of the journey? Answer, 3,300 miles. 12. The Buffalo made 300 miles in one day, which was 4% of her trip. What was the length of her trip? Answer, 7,500 miles. 13. A pump discharged 782 gallons of water per minute, which was 16% of the capacity of the pumping machinery on the ship. What was the total capacity? Answer, 4,692 gallons. 14. A torpedo-boat destroyer is making 27 knots, which is 81% of her best speed. What is her best speed? Answer, 33 knots. 15. The West Virginia had 1,260 tons of coal aboard, which was 60% of her capacity. What was her capacity? Answer, 2,100 tons. 16. A ship displaced 9,000 tons when launched. This was 334% of her displacement when commissioned. What was her displacement when commissioned? Answer, 27,000 tons. 17. The Smith displaces 740 tons, which is 23% per cent of what the Pennsylvania's displacement will be. What will be the displacement of the Pennsylvania? Answer, 31,600 tons. 18. A ship in making a trip up a river loses 3 knots per hour on account of the current. This is 20% of her speed in still water. What is her speed in still water? Answer, 15 knots.. CASE IV. Given the rate and the amount or difference to find the base. 1. A number plus 35% of itself equals 675. What is the number? |