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hand of a clock was between 6 and 7; within an hour the hands had exactly changed places with each other; when were they in the first position ? Ans. 5 h. 32 min. 18193 sec.
23. When gold was worth 50% more than currency, what was the value in gold of a ten-dollar bill? Wben currency was worth 50% less than gold, what was the value in currency of a gold eagle?
Ans. $63; $20. 24. A room is 20.5 ft. long, 16.7 ft. wide, and 9.5 ft. high; there are 2 windows 5.75 ft. high, and 3.5 ft. wide, and a door 6.6 ft. high and 3} ft. wide. What will be the expense of plastering the room at 31¢¢ a square yard, and of carpeting it with ingrain carpet a yard wide @$1.624? Ans. $96.09.
25. A goldsmith bought an ingot of gold at $192 per lb., and sold it at $16 per ounce, using A voirdupois weight both times. If the true weight of the ingot was 8 lb. Troy, how much did he gain by the fraud, gold being worth $16 an ounce ?
Ans. $421135 26. A steamer going from Philadelphia to Liverpool passes over 81 degrees of longitude on an average in a day; how long is it from noon one day to noon the next day, and how long will it be on the return voyage ?
Ans. 23 h. 26 min. out; 24 h. 34 min. return. 27. Four men make regular excursions into the country, between which each stays at home just one day. A is always absent 3 days, B 5 days, and C and D each 7 days. If they all set out on the same day, how many days will elapse before they can all be at home on the same day ? Ans. 23 days.
28. If of the cost of an article equals 1 of its selling price, what is the loss per cent. ? If f of the cost of an article equals á of its selling price, what is the gain per cent. ?
Ans. 41% ; 5% 29. How many bricks will be required to build a 13 inch wall of average bricks 7 ft. high round a garden containing 2 acres in the form of a square, and what will be the cost of the bricks at the rate of $4} P M., the mortar being of an inch thick, and no allowance made for corners ?
30. B drew out of bank 20% of his deposits, then 30% of the remainder, and afterwards 40% of what then remained, and had $420 left; what was his deposit? Ans. $1250.
31. A, baving a quantity of canal stock, sold 25% of it to B, who sold 33% of his purchase to C, who sold 37% of his purchase to D, who received 5 shares; how many had A at first ?
Ans. 160 shares. 32. A dress-pattern having been cut from a piece of silk, there were left 83 yards, which was 66% less than the quantity cut off; how many yards were there at first?
Ans. 331 yards. 33. A speculator invested $9720 in oil and lost 20%; he then invested the remainder in sugar and gained 25%; he then invested his money in fancy stocks and lost 30% ; did he gain or lose, and how much ?
Ans. Lost $2916. 34. A and B receive equal legacies; A spent 75% of his in land, and B lost in speculation as much as equaled 333% of what both received, and then they had together $350 ; what was the amount of the legacy, and what had each left ?
Ans. Legacy, $600 each ; A, $150; B, $200. 35. A merchant spent equal sums of money in cotton, linen, and woolen goods, and made 10% on the cotton, and 8% on the linen, but lost 25% on the woolens; the whole amount of the sales was $2842.10; what did he pay for each kind of goods ?
Ans. $970. 36. A's gain was 26%, and B's 30%, and A's gain was $27 less than B's; what was the capital of each, if of A's equals of B's ?
Ans. A's $4050; B's $3600. 37. A sold his farm and house for $9000, receiving as much for his house as for his farm; on the farm he gained 7% and on the house he lost 5% ; what was the cost of each?
Ans. House, $4210.526; farm, $4672 897. 38. A broker charged me 24% for purchasing some uncurrent bank-notes at 15% discount. Three bills, of $20, $50, and $100 respectively, turned out to be worthless, but by selling the rest at par I made $85 ; what was the face of the notes?
39. What is the amount of a note for $765.35, dated Aug. 9, 1872, and paid June 12, 1876, interest 7%, payable annually?
Ans. $992.78. 40. Two steamboats leave Philadelphia and Trenton at the beginning of ebb-tide, going towards each other, their rate of travel being 10 miles an hour, and the tide running l} miles an hour; how far from Philadelphia will the boats meet, the distance being about 30 miles? Ans. 123 mi.
41. Three men start from the same point to travel round an island 80 miles in circumference; the first goes 5 miles a day, the second 10 miles a day, and the third goes 10 miles a day in the opposite direction; how long before they will all meet again?
Ans. 16 days. 42. If the shipment of a coal operator for a year was 1800 long tons, and the cost per long ton was for mining 50€, hauling and outside labor 484, incidentals, wear of tools, machinery, etc., 454, royalty on land 50%, freight by railroad $1.75, capital 48%, commission on sales 4%, and the sales averaged $6 per ordinary ton; what was his profit for the year?
Ans. $4608. 43. A gentleman, asking the consent of a lady to marry the second of her five daughters, was told that he should bave her on condition of finding what was the fortune of each daughter by their father's will, which was as follows: the first four had $50,000; the last four, $66,000; the first and last three, $60,000; the first three and last, $56,000; and the first two and last two, $64,000; what were their fortunes? Ans. $8000; $14,000; $10,000; $18,000; $24,000.
44. A company engaged an agent to do business for one month at a salary of $25, giving him goods amounting to $57.54 and $32.17 in cash to start with. The agent bought during the month goods amounting to $59.91. At the end of the month the goods on hand amounted to $31.67, and the amount of sales for the month was $102.97; required the balance of the account. Ans. Loss to company, $7.81.
45. In 1869 it is estimated that 550,000,000 feet of lumber was manufactured in the Saginaw Valley, at a profit of
$375,000; what was the rate per cent. of profit, if the capital invested was in mill property $3,754,000, in shingle mill property $295,500, and in tools, teams, slides, etc., estimated at $4 per M. feet of lumber made ?
Ans. 6% + 46. A tailor sold 11 garments for $77, viz.: coats at $13, pants at $6, vests at $5, and cravats at $3 each; required the number of each.
Ans. 3, 4, 1,
3. 47. Mr. Johnson invested a certain amount in cotton, and Mr. Wilson invested 3 times as much ; Mr. Johnson lost 20%, wbile Mr. Wilson gained 25%, and the difference between the amounts they received was $885; how much did each invest?
Ans. $300; $900. 48. A retail merchant sold a quantity of silks for $1078.12., thereby gaining 20%; the wholesale merchant from whom he bought them made a profit of 15%; and the importer who sold them gained 25%; what did they cost the importer?
Ans. $625. 49. A traveler journeyed 500 miles in two days, and s of the distance he traveled the first day, plus of the distance he traveled the second day, equals of the distance he traveled the first day; how far did he travel each day?
Ans. 24131 miles; 258,1 miles. 50. What sum must a man save annually, commencing at 21 years of age, to be worth $50,000 when he is 50 years old, investing his money yearly at 6% compound interest?
Ans. $678.98. 51. A, B, and C formed a partnership; A put in $500 for 8 months, B, $750 for a time unknown, and C, an amount not known for 10 months; what were B's time and C's stock, if A received $580 for his stock and profit, B, $840 for his stock and profit, and C, $720 for his stock and profit?
Ans. B, 6 months; C, $600. 52. A railroad has been constructed through a farm, making it necessary to build fences at a cost of $750, which must be renewed every 15 years; what should the owner receive to meet this expenditure, at 6% compound interest ?
53. A gentleman having 4 sons, left the youngest $5000, the eldest $7200, and the two others the arithmetical and geometrical means of these sums respectively; what were the shares of the other sons ?
Ans. $6000; $6100. 54. Two adjoining farms rent for $400 a year, rent being paid in the one case semi-annually, and in the other quarterly; what would be the difference in the amount of the rent of each for 25 years, int. 8% ?
Ans. $689.81. 55. Mr. Smith bought a house for $3000, agreeing to pay for it in annual payments of $500 each ; but finding himself unable to make the payments, and having the reversion of a perpetuity in 12 years, he makes an agreement with bis creditors to pay the whole amount with compound interest at 6% when he enters upon his perpetuity; what amount will then be due ?
Ans. $6036.59 56. Two drovers met on the road, when one said to the other, Give me one of your steers and I shall have twice as many as you then have. But, replied the other, if you give me one of yours, I shall have as many as you. How many had each?
Ans. 7; 5. 57. A man gave me his note for $500, payable in 8 years, interest at 6%; if he pays the interest annually, to what rate is this equivalent, if the same amount of interest had been paid at the end of the time ?
Ans. 78%. 58. A tailor bought 50 yards of broadcloth 14 yards wide, but on sponging, it shrunk 5% in width, and 5% in length; to line it he bought flannel 1: yards wide, which shrunk 1 yard for every 20 yards in length and t of a yard in width; how many yards of flannel are required? Ans. 571% yd.
59. A planter hired 75 persons for $90, giving the men $3, the women $1}, the boys $), and the girls $f a day; how many were there of each ?
21, 6, 6, 42: 18, 12, 36, Ans.
9: 19, 11, 18, 27: 15, 24, 18, 18. 60. In turning a cart within a circle, it was observed that the outer wheel made two turns while the inner made but one; the wheels were each three feet bigh, and the axle-tree