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............... A + B + C do

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.. time in which A+B+C would finish the work

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days=1103 days.

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107

210

11

Again, in one day A + B do (+1), or, of the work; therefore time

in which they would finish it=or 2 days.

11

30

In like manner, it may be shewn that A and C would finish the work in 211 days; and B and C in 3 days.

Ex. 19. It being given that A and B can do a piece of work in 2 days; that A and C can do the same in 21 days; and that B and C can do it in 3 days: find the time in which A, B, and C would do the work: working, first, all together, secondly, separately.

.. by addition,

11

In one day A and B do

of the work,

30

12

A and C do

35

13

B and C do

42

In one day 24+2B+2C would do (+12+13),

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work done by A+B+C in one day-work done by B+C in one day,

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therefore time required, in which A would do the work,

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In like manner it may be shewn, that B would do the work in 6 days, and that C would do it in 7 days.

Ex. 20. A cistern is fed by a spout which can fill it in 2 hours, how long would it take to fill it if the cistern has a leak which would empty it in 10 hours?

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Therefore in one hour, when the spout and leak are both open, the part of the cistern filled by what runs in- what runs out,

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Ex. 21. A can perform a certain quantity of work in 5 days, B twice as much in 6 days, and C 4 times as much in 9 days; in what time can A, B, and C working together, perform a piece of work 11 times as great?

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44

.. they would finish this piece of work in days,

.. they would finish required piece of work in (4 × 11) or 114 days.

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Ex. 22. A and B can do a piece of work in 15 and 18 days respectively; they work together at it for 3 days, when B leaves, but A continues, and after 3 days is joined by C, and they finish it together in 4 days; in what time would C do the piece of work by himself?

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.. time in which C would do the whole work = 24 days.

Ex. LV.

1

24'

Miscellaneous Questions and Examples on preceding Arts.

I.

1. State the rules for the multiplication and division of decimals, and divide 34 17 by 31.

2. What is the value in English money of 1556-85 francs, when the exchange is at 24°25 francs per £?

3. Reduce +++ to a decimal fraction. What decimal of a cwt. is 1 qr. 7 lbs. ?

4. Explain the principle of the Rule of Practice. Find (by Practice) the cost of 365 tons of coals at 13s. 5 d. a ton; and the rent of 315 ac., 3 ro., 7 po. at £1. 16s. 8d. an acre.

5. If of an estate be worth £1003. 17s. 1d., what is the value of of it?

6. If a bankrupt pay 3s. 4d. in the pound, what will be received on a debt of £3678. 16s.?

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7. A person possessing of an estate, sold of of his share for

£120g; what would

of

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of the estate sell for at the same rate?

8. A man, his wife, and 3 children earn £1. 7s. 6d. a week; the wife earns twice as much as each child, and the man three times as much as his wife; required the man's weekly earnings.

9. If £1. sterling be worth 12 florins, and also worth 25 francs, 56 centimes; how many francs and centimes is one florin worth? (100 centimes=1 franc.)

10. The wages of 5 men for 6 weeks being £14. 5s., how many weeks will 4 men work for £19?

II.

1. What is meant by saying that one sum is a certain fraction (for example) of another? If 26 francs are equivalent to a pound, what fraction of a shilling is a franc? Give the reasons for the process which you adopt in answering the question.

2. Express of 15 of a mile in terms of a metre, supposing 32 metres 35 yards.

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3. A, B, and C rent a pasture for £40. A puts in 8 cattle, B, 9, and C, 11: how much should each pay for his share?

4. Reduce 3 d. to the decimal of 10s., and divide the result by 12·5. Explain the process employed.

5. Find the value of 45 ac., 3 ro., 20 po. at £111. 11s. 4d. per acre, by Practice.

6. If the property in a town be assessed at £60000, what must be the rate in the £ in order that £2500 may be raised?

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7. If the circumference of a circle Diameter x 3.14159; find the number of revolutions passed over by a carriage-wheel 5 ft. in diameter in 10 miles.

8. A farmer has to pay yearly to his landlord the price of 7 bushels of wheat at 4s. 9d. per bushel, and 91 of malt at 5s. 3d., and 63 of oats at 28. 4d. What is the whole amount of his rent?

If there were a decimal coinage of pounds, florins, &c., how many of them would he have to pay?

9. A alone can do a piece of work in 10 hours, and B can do it in 12 hours, find the time in which both working together can do it.

10. Ten excavators dig 12 loads of earth in 16 hours, whilst 12 others

can dig only 9 loads in 15 hours; in what time will they jointly dig 100 loads?

III.

1. Divide 28 tons, 4 cwt., 3 qrs. into 36 equal portions; and find the value of one of them at £7. 10s. 8d. per cwt.

2. Reduce 186 yds., 2 ft., 8 in. to the decimal of a chain. If one chain=10 chainlets=100 links 1000 linklets; express the above in chains, chainlets, links, linklets.

3. If £1 sterling be worth 45 Pauls, 9 Baiocchi (Roman), and be worth 25 francs (French); shew that a Napoleon of 20 francs = 36 Pauls. (10 Baiocchi=1 Paul.)

4. If the rents of a parish amount to £2514. 7s. 6d. and a rate is granted of £83. 16s. 3d., how much is that in the £? and how much must be paid by an estate whose rental is £115. 12s. 6d. ?

5. If a tradesman with a capital of £1000 gains £90 in 7 months, in what time will he gain £20. 5s. with a capital of £315?

6. What is the difference between simple and compound Practice? Required the price of 3 cwt., 3 qrs., 16 lbs. at £4. 6s. 03d. per quarter, by Practice.

7. Determine the expense of papering a room 12 ft. high, measuring 20 ft. by 15 ft., at the rate of 21d. per square yard.

8. In the civil year 97 days are intercalated in 400 years; what is the average length of the year?

9. If 15 horses and 148 sheep can be kept 9 days for £75. 15s., what sum will keep 10 horses and 132 sheep for 8 days, supposing 5 horses to eat as much as 84 sheep?

10. A, B, and C are three workmen: A can do half a piece of work in 3 hours, being twice as much as B can do ; and A, B, and C can together do the whole in 2 hours. Shew that C can do in 5 hours as much

as B can do in 9 hours.

IV.

1. Explain how whole numbers are represented in the decimal or common system of notation. Multiply 729 by 37, and explain the process.

2. Add together the fifth of a shilling, two-sevenths of a crown, and four-ninths of a guinea; and reduce the result to the decimal of £25.

3. Two persons gained in trade £375; one having put in £500 and the other £850; what part of the profit ought each person to receive?

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