EXAMPLES. 1. Suppose there are 4 companies, in each of which there are 9 men; it is required to find how many ways 4 men may be chosen, one out of each company. 66 81 9 729 9 6561 Or, 9X9X9X9=6561 the answer. 2. Suppose there are 4 companies, in one of which there are 6 men, in another 8, and in each of the other two 9; what are the choices, by a composition of 4 men, one out of each company? Ans. 3888. 3. How many changes are there in throwing 5 dice? Ans. 7776. MISCELLANEOUS QUESTIOAS. 1. WHAT difference is there between twice five and twenty, and twice twenty-five? Ans. 20. 2. A was born when B was 21 years of age; how old will A be when B is 47; and what will be the age of B when A is 60 ? Ans. A 26, B 81. 3. What number, taken from the square of 48, will leave 16 times 54 1 Ans. 1440. 4. What number, added to the thirty-first part of 3813, will make the sum 200? 1 Ans. 77■ 5. The remainder of a division is 325, the quotient 467, and the divisor is 43 more than the sum of both what is the dividend? Ans. 390270. 6. Two persons depart from the same place at the same time; the one travels 30, the other 35 miles a day: how far are they distant at the end of 7 days, if they travel both the same road; and how far, if they travel in contrary direcAns. 35, and 455 miles. tions? 7. A tradesman increased his estate annually by 1001. more than part of it, and at the end of 4 years found, that his estate amounted to 103421. 3s. 9d. What had he at first? Ans. 40001. 8. Divide 1200 acres of land among A, B, and C, so that B may have 100 more than A, and C 64 more than B. Ans. A 312, B 412, and C 476. 9. Divide 1000 crowns; give A 120 more, and B 95 less, than C. Ans. A 445, B 230, C 325. 10. What sum of money will amount to 1321. 16s. 3d. in 15 months, at 5 per cent. per annum, simple interest? Ans. 1251. 11. A father divided his fortune among his sons, giving A 4 as often as B 3, and C 5 as often as B 6; what was the whole legacy, supposing A's share 50001. Z B Ans. 118751. 12. If 1000 men, besieged in a town with provisions for 5 weeks, each man being allowed f6 oz. a day, were reinforced with 500 men more. On hearing, that they cannot be relieved till the end of 8 weeks, how many ounces a day must each man have, that the provision may last that time? Ans. 6| oz. be added, ៖ Ans. 53 13. What number is that, to which if of the sum will be 1? 14. A father dying left his son a fortune, of which he ran through in 8 months; of the remainder lasted him twelve months longer; after which he had only 4101. left. What did his father bequeath him? Ans. 9561. 13s. 4d. 15. A guardian paid his ward 35001. for 25001. which he had in his hands 8 years. What rate of interest did he allow him? Ans. 5 per cent. 16. A person, being asked the hour of the day, said, the time past noon is equal to of the time till midnight. What was the time? Ans. 20 min. past 5. 17. A person, looking on his watch, was asked, what was the time of the day; he answered, it is between 4 and 5; but a more particular answer being required, he said, that the hour and minute hands were then exactly together. What was the time? Ans. 21 minutes past 4. 18. With 12 gallons of Canary, at 6s. 4d. a gallon, I mix^ ed 18 gallons of white wine, at 4s. 10d. a gal. and 12 gallons of cider, at 3s. Id. a gal. At what rate must I sell a quart of this composition, so as to clear 10 per cent, ? Ans. Is. 3 d. 19. What length must be cut off a board, 8 inches broad, to contain a square foot, or as much as 12 inches in length and 12 in breath? Ans. 171 in. 20. What difference is there between the interest of 3501. at 4 per cent. for 8 years, and the discount of the same sum at the same rate and for the same time? Ans. 271. 3. 21. A father devised of his estate to one of his sons, and of the residue to another, and the surplus to his relict for life; the children's legacies were found to be 2571. 5s. 4d. different. What money did he leave for the widow? Ans 6351. 10 d. 2240 22. What number is that, from which if you take \ of 3, and to the remainder add of, the sum will be 10? Ans. ity,vv 23. A man dying left his wife in expectation, that a child would be afterward added to the surviving family; and making his will ordered, that, if the child were a son, his estate should belong to him, and the remainder to his mother; but if it were a daughter, he appointed the mother of , and the child the remainder. But it happened, that the addition was both a son and a daughter, by which the widow lost in equity 24001. more than if there had been only a girl. What would have been her dowry, had she had only a son? Ans 21001. 24. A young hare starts 40 yards before a grey-hounA, and is not perceived by him till she has been up 40 seconds; she scuds away at the rate of ten miles an hour, and the dog, on view, makes after her at the rate of 18. How long will the course continue, and what will be the length of it from the place, where the dog set out? Ans. 60 seconds, and 530 yards run. 25. A reservoir fbr water has two cocks to supply it; by the first alone it may be filled in 40 minutes, by the second in 50 minutes, and it has a discharging cock, by which it may, when full, be emtied in 25 minutes. Now supposing, that these three cocks are all left open, that the water comes in, and that the influx and efflux of the water are always alike, in what time would the cistern be filled? Ans. 3 hours 20 min. 26. A sets out from London for Lincoln precisely at the time, when B at Lincoln sets forward for London, distant 100 miles; after 7 hours they met on the road, and it then appeared, that A had ridden 1 mile an hour more than B. At what rate an hour did each of them travel? Ans. A 7, B 6|| miles. 27. What part of 3d. is a third part of 2d. Ans. 28. A has by him 14cwt. of tea, the prime cost of which was 961. sterling. Now granting interest to be at 5 per cent. it is required to find how he must rate it per pound to B, so that by taking his negotiable note, payable at 3 months, he may clear 20 guineas by the bargain? Ans. 14s. 1d. sterling. 29. What annuity is sufficient to pay off 50 millions of pounds in 30 years, at 4 per cent. compound interest? Ans. 28915051. 30. There is an island 73 miles in circumference, and 3 footmen all start together to travel the same way about it; A goes 5 miles a day, B 8, and C 10; when will they all come together again? Ans. 73 days. SI. A man, being asked how many sheep he had in his drove, said, if he had as many more, half as many more, ane 7 sheep and a half, he should have 20: how many had he? Ans. 5. 32. A person left 40s. to 4 poor widows, A, B, C, and D; to A he left, to B ^, to C \, and to D, desiring the whole might be distributed accordingly: what is the proper share of each? 16 Ans. A's share 14s. 11. B's 10s. 6d. C's 8s. 5j£d. D's 7s. d. 33. A general, disposing of his army into a square, finds he has 284 soldiers over and above; but increasing each side with one soldier, he wants 25 to fill up the square; how many soldiers had he? Ans. 24000. 34. There is a prize of 2121. 14s. 7d. to be divided among a captain, 4 men, and a boy; the captain is to have a share and a half; the men each a share, and the boy of a share: what ought each person to have? Ans. The captain 541. 14s. d. each man 361. 9s. 4 d. and the boy 121. 3s. l d. 35. A cistern, containing 60 gallons of water, has 3 unequal cocks for discharging it; the greatest cock will empty it in one hour, the second in 2 hours, and the third in 3: in what time will it be empty, if they all run together? Ans. 32 minutes. 36. In an orchard of fruit trees, of them bear apples, pears, plumbs, and 50 of them cherries: how many trees are there in all * Ans. 600. 37. A can do a piece of work alone in ten days, and B in 13; if both be set about it together, in what time will it be finished? Ans. 51 days. |