(73) If I pay £13. 13s. per quarter for rent, £2. 8s. 6d. per quarter for rates, £2. 18s. 9d. a-week for food, 11s. 3d. a-week for washing, £42 every half-year for school bills, £15. 128. 6d. every half-year for life insurance, £35 a-year for clothes, £3. 10s. for coals for the summer half and £7. 7s. for the winter half-year, and wish to lay by £120 out of an income of £600 a-year, how much shall I have for other expenses? (74) A publisher sells a certain book at 38. 2d. per copy nett; of this, he pays to the printer, 94d. per copy; to the binder, 63d. per copy; to the author, a royalty of 9d. for every copy he sells. Of an edition of 1000 copies, he sells 853; the remainder are left on hand. Will he have lost or gained, and how much? (75) I bought 2 tons of sugar at 31d. per lb. ; 7 cwt. 21 lbs. got damaged. I sold the good sugar at 4d. a pound, and the damaged sugar at 2d. per pound. What was my gain or loss? (76) A person mixed 23 gallons of Jamaica rum at 9s. 7d. per gallon, with 18 gallons of British rum at 7s. 5d. per gallon, and 30 gallons of water; he sold the mixture at 11s. 6d. per gallon. What was his total gain? (77) A person bought 427 yards of cloth at 3s. 8d. per yard; for how much must he sell the whole so as to gain 7d. per yard? (78) If 8 articles cost £4. 78. 101d., what will 56 articles cost? (79) If 9 men can dig 43 yards of trench in a given time, how much will 45 men dig in the same time? (80) How much in double the time? (81) If 3 men build a given wall in 14 days, how long would 1 man take to build it? (82) If 20 men build a given wall in 8 days, how long will 10 men take to do it? (83) And how long would 4 men take? (84) If 3 articles cost 118. 8d., what will 27 articles cost? (85) If 8 chairs cost £2. 2s. 6d., what will 64 chairs cost? (86) If one dozen pens cost 31d., what will the gross cost? (87) A man bought 28 Bandana handkerchiefs at 7 for £1. 12s. 71⁄2d.; he sold them at 5s. 9d. each. Find his total profit. (88) By mistake he entered this profit in his books among the losses; at the end of the month his books shewed a profit of only £83. 10s. What ought they to have shewn? (89) In a given time 9 men can put up 67 yards of fence. How many yards can 63 men put up in treble the time? (90) If 17 men can dig a given quantity of trench in a given time, how many men will be wanted to dig 4 times the quantity in a quarter of the time? (91) If out of a sack of flour we make 43 shilling loaves, how many threepenny loaves could we have made of it? (92) Simplify 17 x (18447 +62). (93) Simplify 302 × (5 × 17 — 3 × 11); 597 × (5 x 17 9 x 9). (94) Simplify 6 × 7 × (11 × 156 + 13 × 84). (95) Simplify (81 + 317) × (24 + 11). (96) Simplify 6x8x9x5x4 x 317. (97) Find the continued product of the first 9 numbers. (98) Shew that 740625 × 386 + 740625 × 234 + 740625 × 1671 + 740625 × 176 + 740625 × 809 + 740625 × 546 = 740625 × 546 × 7. (99) Shew that £7.8s. 11⁄2d. × 386 + £7. 8s. 11⁄2d. × 234 + £7.8s. 11⁄2d. × 1671 + £7. 88. 11⁄2d. × 176 + £7. 8s. 11⁄2d. × 809 + £7. 8s. 11⁄2d. × 546 = £7. 8s. 11⁄2d. × 546 × 7. (100) A bankrupt owes £8745, and can pay 9s. 5ąd. in the £1. What are his assets? (101) A railway company has 16,200 shares. Their expenses are £14,175. What must be the company's gross income to yield a dividend of 178. 6d. per share? (102) Multiply the sum of 438619 and 30405 by 198. (103) Multiply the difference between 438619 and 30405 by 1098. (104) Multiply the sum of 2815 and 365 by the difference between these two numbers. (105) From 18 times the product of 519 and 98 take 7 times this product. How many times are 112 lbs. contained in 800 lbs. ? How many men will it require to dig 41 yards of trench in a given time if 1 man can dig 6 yards in that time? Six men would in the given time leave 5 yards to be done, seven men would be able to do 1 yard more than required; we may choose either answer, but 7 men is the more correct. Ans. 7 men and 1 yard to spare. The process by which we find the number of times that one quantity is contained in another is called Division, for which the symbol is. 2. Learn by heart: This sign (÷) is called DIVIDED BY, and has the following meaning: Find HOW MANY TIMES the quantity following the sign is contained in the quantity preceding the sign, and the answer will be so MANY TIMES. 3. Learn by heart: In Division the quantity to be divided is called the DIVIDEND, that by which we divide is called the DIVISOR, and the answer is called the QUOTIENT. If anything is over it is called the REMAINDER. EXERCISE XIX. (1) How many times are £5. 7s. 11d. contained in £16. 38. 9d.? (2) £13. 13s. 10d. ÷ £3. 8s. 51d. (3) If 1 article costs 12s. 7 d., how many can I buy for £4. 88. 4 d. ? (4) If I save £1. 48. 10d. a-week, how long shall I be in accumulating £9. 198. ? (5) By what number must I multiply £8. 48. 6d. to make £41. 2s. 6d.? (6) To how many persons can I give £3. 15s. each out of £37. 10s.? (7) If I can travel 65 miles a-day, how long will it take me to get over 520 miles? (8) If one strip of carpet is 115 inches in length, how many strips can I cut from 1035 inches of carpet? (9) How many regiments of 875 men each are there in 9625 men? (10) How many yards of wall can I build with 448 bricks if each yard requires 64 bricks? (11) How many times are £3. 8s. 10d. contained in £15 ? (12) £37. 9s. 4d. ÷ £4. 13s. 7d. (13) If 1 article costs £1. 5s. 9d., how many can I buy for £8. 1s. ld.? |