Ex. 4. The sum of £463. 16s. is to be raised in a parish, the assessment of which is £6184; what is the rate in the £.? Ex. 5. After taking from my purse of my money, I find that of what is then left amounts to 7s. 6d.; what money had I in my purse at first? Let unity, or 1, denote the sum in the purse at first. away, remains. Now by the question After taking Ex. 6. A met two beggars, B and C; and having of a moidore in his pocket, gave B 177 remainder; what did each receive? 3 3 of of that sum, and C of the 5 Ex. 7. A farmer pays a corn-rent of 5 quarters of wheat and 3 quarters of barley, Winchester measure: what is the money value of his rent, when wheat is at 60s., and barley at 54s. per quarter, imperial measure; 32 imperial gallons being = 33 Winchester gallons? Rent is 5 qrs. of wheat Win. mea. +3 qrs. of barley Win. mea. Ex. 8. If £1. sterling be worth 25 francs, 60 centimes; and also worth 6 thalers, 20 silber groschen; how many francs and centimes is a thaler worth? (One thaler=30 silber groschen, 1 franc=100 centimes.) 6 thalers, 20 silber groschen=25 francs, 60 centimes, Ex. 9. Standard gold contains 12 parts of pure gold to one part of copper, and 20lbs. Troy are coined into 934 sovereigns and a halfsovereign; find the weight of pure gold in a sovereign. 12 Number of parts=12+1=13, of which is pure gold. By the question, 13 Ex. 10. If a person, travelling 133 hours a day, perform a journey in 27 days, in what length of time will he perform the same if he travel 10 hours a day? * If he travel 132 hrs. a day, he does the journey in 27ğ days, Ex. 11. If 858 men in 6 months consume 234 quarters of wheat, how many quarters will be required for the consumption of 979 men for three months and a half? 858 men in 6 months consume 234 quarters, Ex. 12. If 5 men or 7 women can do a piece of work in 37 days; in what time will 7 men and 5 women do a piece of work twice as great? Now by the question, 7 women in 37 days do the piece of work, .. 1 woman in (37 × 7) days does Ex. 13. A bankrupt owes three creditors A, B, and C £250, £330, and 400 guineas respectively, and his property is worth £125; how much will each creditor receive, and how many shillings in the pound? Debts amount to £(250+330+420), or £1000. .. A gets £31. 5s., B gets £41. 5s., and C gets £52. 10s. He pays of £1., or 2s. 6d., in the £. Ex. 14. Gunpowder being composed of nitre 15 parts, charcoal 3 parts, and sulphur 2 parts; find how much of each is required for 16 cwt. of powder, The whole number of parts (15+3+2)=20. Of every 20 parts, .. 15 3 20 4 3 3 20 of 16 cwt., or 12 cwt. = quantity of nitre required. of 16 cwt., or 2 cwt.............charcoal Ex. 15. The price of a work which comes out in parts is £2. 16s. Ed. But if the price of each part were 13d. more than it is, the price of the work would be £3. 78. 6d. How many parts are there? £2. 16s. 8d.+(number of parts × 13) d. = £3. 7s. 6d. .. (number of parts x 13) d. = 10s. 10d. =130d. .. number of parts=130=10. Ex. 16. Divide 1860 guineas between A, B, and C, so that as often as A gets £5., B shall get £4., and as often as B gets £3., C shall get £1. It is clear that B's share=3 times C's share, 4 times A's share=5 times B's share, but A's share + B's share + C's share=1860 guineas; 15 4 C's share +3 C's share + C's share=1860 guineas, of the kings are of the same name, of a fourth, and there are 5 besides: how Ex. 17. Of a certain dynasty, of another, of a third, and many are there of each name? Representing the whole dynasty by unity, or 1. 5 24 But by the question, 5 24 of unity, or of the whole dynasty=5; .. 1, or the whole dynasty, =5×2=24; ..there are 8 kings of the 1st name, 6 of the 2nd, 3 of the 3rd, and 2 of the 4th. Ex. 18. A can do a piece of work in 5 days, B can do it in 6 days, and C can do it in 7 days; in what time will A, B, and C, all working at it, finish the work? Find also in what time A and B working together, A and C together, and B and C together, could respectively finish it. Representing the work by unity, or 1. In one day 4 does part of the work, |