(233) Find the present worth at 4 per cent. compound interest of an annuity of £311 48. 10d. payable for 4 years, the first payment being due in 6 months' time. (234) Find the diagonal, and the area of the diagonal plane, of a cube whose volume is 3 cubic feet. (235) A having £1000 in the funds sells out at 831 and lends the money to B for two years at 5 per cent., with the condition that at the end of the time the principal is to be repaid as £1000 stock. At the end of the time the funds have risen to 88%, what amount in principal and interest will B have to pay, brokerage per cent. being taken into account for each transaction? I 8 (236) The workmen in a factory are employed 10 hours a day, and receive 32s. 6d. per week wages; how much per cent. will the amount paid in wages be increased for the performance of the same work, if the time is diminished by half an hour, and the wages increased by 1d. per day? (237) A bill is due in 2 months, and interest is reckoned at 4 per cent.; what fractions of the principal are the interest and the true discount? Find the price of stock when £325 stock can be paid for by a bill of £314 128. due as above, true discount being allowed. (238) A plumber finds that the materials for making a cubical cistern cost him £10; how much will he have to pay for the materials of two similar cisterns which shall each contain half that quantity of water? (239) How far might be seen from the top of a mountain 4 miles high, the diameter of the earth being 7920 miles? (Eucl. III. 36.) (240) The papering of a room cost £1 17s. 6d., find the cost of papering another room whose length, breadth, and height are each half as much again, the paper being half as wide again, and the price per yard twice as much. (241) Two sums of money are to be divided among three persons, one equally and the other in the proportion of 3, The shares of the first two amount to £13 98. and £16 198. determine the sums. 5, 8. (242) The circumferences of the wheels of a carriage are 6 ft., and 8 ft., what is the least distance in which each wheel will turn a complete number of times? If A and B are the lowest points of the two wheels at starting, how often will they touch the ground together in going 10 miles, and at what distance before the end will this last happen? (243) If 5 excavators sink a circular shaft 8 feet in diameter and 125 fathoms deep in 100 days of 10 hours each, how many nights of 7 hours each will 4 excavators be in sinking one 6 feet in diameter and 75 fathoms deep; the difficulty of working by night being one-seventh greater than by day and the hardness of the latter ground being to that of the former as 7: 5? (244) A person borrows a sum of money at 5 per cent., and repays it with its interest in four annual payments of £810 68. 9d. Find the amount of the debt. (245) A's rate of working: B's :: 7 : 5, B's : C's :: 4: 3, and C's D's :: 5 : 6. A's time each day: B's::9: 10, B's C's 10: 11, and C's: D's :: 10: 7. Also A's number of days: B's :: 15: 7, B's: C's :: 11: 20, and C's: D's 75. How should £305, which is to be paid for the whole work, be divided between them? (246) A contractor undertook to build a house in 84 days, and engaged 30 men to do the work. But after 40 days he found it necessary to engage 20 men more, and then he completed the work 2 days too soon. How many days behindhand would he have been if he had not engaged the additional men? (247) A sum may be invested at once in stock yielding 3 per cent. per annum, at 94; or at the end of two months it may be invested in shares at par which will yield 4 per cent. per annum. Supposing the interest in each to be paid monthly, in what time would the return from the latter investment be equal to the return from the former? (248) A kilogram (=1000 grams) of French standard gold, which contains 90 per cent. of fine gold, is coined into 155 napoleons. The mint price of English standard gold, which is 22 carats fine, is £3 178. 10d. per ounce. A gram being equal to 15'432 grains, find the value of a R napoleon at the English mint, neglecting the value of the alloy. (249) The length of an iron cylindrical vessel with closed ends is a yard, and its outside circumference 40 inches, the metal being an inch in thickness. Find its weight when filled with water, iron being 7 times heavier than water, and water 62 lbs. per cubic foot. (250) The time of oscillation of a pendulum varies as the square root of its length, and the seconds pendulum is 39 1393 inches long: find the length of the pendulum which oscillates 80 times in a minute. (5) Eight hundred and twenty-nine thousand and seventeen. (6) Eight millions, fourteen thousand, three hundred and twenty-five. (7) Nine hundred and four millions, two hundred and eighty-seven thousand, six hundred and forty-three. (8) Two thousand and ten millions, three hundred and four thousand. (9) Twelve millions and four. (10) 50103. (12) 1000060. (14) 2,406,390,770. (16) 12120012. (11) 2,000,030,100,049. (13) 13001. (15) 10010010. (17) Ninety-seven millions, two hundred thousand, one hundred and two. (18) Three hundred and twenty-six thousand eight hundred and ten millions, twelve thousand and four. (19) 40010706. Ex. 2. (20) 1110005. (12) 9. (8) £303 108. 34d.; 872 gs. 38. oid. (13) 120960; 840000. (15) 32316; 94861. (14) 47174400; 1552320. (16) 196780; 4098048. (17) 2205240; 42793200. (18) 1531200; 120058848. |