Civil service guide

6. The annual consumption of brandy in a country is 4500000 gallons, and the duty is 9s. 2d. per gallon; the duty is reduced 5 per cent., and then the consumption is increased 7 per cent., how is the revenue affected?

7. Convert and to decimal fractions. Divide the first result by the second, and convert the quotient into a vulgar fraction in its lowest terms.

8. Express of a square mile, 2 of a rood, and of a pole, in acres, roods, and poles.

9. If £82 10s. of 34 per cent. stock be assigned to a fund-holder instead of £100 in the 3 per cents., how much per cent. is taken from his income? 10. A London merchant owes the sum of £3500 to another in Paris; what is his gain if instead of sending direct he remits the money from London to Venice, from Venice to Hamburg, from Hamburg to Paris, the exchange being £1 = 24.6 francs; 19 francs = 10 Hamburg merks; 1 Hamburg merk = 4 lires of Venice; 55 lires = £1?

11. A wine which contains 7 per cent. of spirit, is frozen, and the ice which contains no spirit being removed, the proportion of spirit in the wine is increased to 8 per cent., how much water, in the shape of ice, was removed from 504 gallons of original wine?

12, A pound is the weight of 27.7274 cubic inches of water at 62°, and a kilogram the weight of water at 39°, which will fill a cube of which each edge is one decimetre, or 3.937 inches long; find the weight of a kilogram in pounds to 5 places of decimals, taking the expansion of water at '00005 of its volume for every degree of rise in temperature?

Given May 1869.

(Time, 2 hours.)

1. Two lines are 41 06328 and 0438 of an inch long respectively: how many lines, as long as the latter, can be cut off from the former? What will be the length of the remaining line? (a).

2. Explain the terms "interest" and " discount," and find the difference between the interest and discount on £1106 15s., in half-a-year, at 5 per cent.

2. A person's net income, after paying 4d. in the pound income tax, is £1152 13s. 4d., find his gross income.

4. Find the cost of painting the walls of a room, at 9 per square yard, whose length is 17 feet 1 inch, breadth 18 feet 10 inches, and height 12 feet 3 inches.

5. The content of a cube is 450 feet 1088 inches, find its edge.

6. Multiply, duodecimally, 9 feet 11 inches 7 parts by 11 feet 7 inches 9 parts, and the result by 3 feet 4 inches, and give the result in cubic feet and inches.

7. A person converts £27851 17s. 3d. into three per cent. stock, at 78%, and invests the same sum in a 3 per cent. stock, at 95: he sells out when the former has risen per cent., and the latter has fallen per cent. ; how much has he gained? (b)

(a) See Civil Service Arithmetic, p. 235, No. 1. (b) See do., p. 202, No. 233.

8. Find the value of 5.49 × 0318 × 047619 of 25 guineas. 9. A can copy 6 pages while B is copying 5, B copies 15 while C is copying 12, and C can copy 4 while D is copying 3. A, who can write 20 pages a day, receives a paper of 240 pages to copy, and, after doing one-fourth of it, calls in B, C, and D, to assist him: in what time will they have it finished? (a)

10. A cask whose weight is 2 cwts. 12 lbs. oz., is floating in a square cistern whose edge is 2 feet 6 inches; if the cask be removed, how far will the water sink in the cistern, a cubic foot of water being 1000 ounces? (b)

11. 3 men whose strides are 2 feet 8 inches, 3 feet, and 3 feet 4 inches respectively, walk a mile together; how often will they step together in this distance?

12. Bronze contains 91 per cent. of copper, 6 per cent. of zinc, and 3 per cent. of tin; a mass of bell-metal (consisting of copper and tin only) and bronze fused together, is found to contain 88 per cent. of copper, 4.875 per cent. of zinc, and 7·125 of tin, find the proportion of copper and tin in bell-metal. (c)

DUODECIMALS AND MENSURATION.
Specimen Paper.

1. Multiply, by the method of duodecimals, 46 feet 5 inches 4 parts by 9 feet 7 inches 8 parts.

2. Express the result obtained in the last question in square feet, square iuches, and a fraction of the square inch.

3. Multiply 5 feet 3 inches by 6 feet 7 inches, and the product by 7 feet 11 inches, What is the actual value of the denomination which occupies the place of inches in this product?

4. The diagonals of a diamond-shaped garden are 79 and 84 yards. Find its value at £121 per acre.

5. Find the number of acres, &c., contained in a four-sided field, having given the diagonal equal to 15 poles, and the two perpendiculars on it from the opposite angles, equal to 53 and 67 poles respectively. 6. The side of a hexagonal field is 247 yards. Find its value at £80 13s.

4d. per acre.

7. A circular piece of ground contains an acre. 13 feet radius, turn in going round it?

How often will a wheel,

8. The longest and shortest diameters of an elliptical

lawn are 94 and

67 yards; and the carriage-drive round it is 17 feet wide.
the area to be gravelled,

Find

9. A railway cutting is 38 feet wide at the bottom and 74 at the top, 35 feet deep, and of a mile long. How many solid yards of earth were removed?

10. Give the rules for finding the solid contents of a sphere, spheroid, cone, and frustrum of a pyramid.

(a) See Civil Service Arithmetic, p. 178, No. 25. (b) See do. p. 176, No. 7. (c) See do. P. 237, No. 12.

11. A rectangular bar of metal is bent into a wheel. Its outer and inner diameters are 44 and 26 inches, and its thickness 6 inches; find

its solid content.

12. The diameter of a pipe by which a cistern is being emptied is 6 inches

at one end, and 2 at the other. The water is flowing 6 miles an hour as it enters at the large end; find with what velocity it will escape from the small one.

13. A block of stone forms the frustrum of a square pyramid. The perimeter of its base is 28 feet, and its top is 20 feet, and its height is 36 feet. Find its value at 40s. 6d. a solid yard.

14. Describe the protractor, vernier, and theodolite, and explain their uses.

WEIGHTS AND MEASURES.

Specimen Paper.

1. Mention the names of the several weights employed (1) in troy measure, (2) in avoirdupois measure.

2. What is the value of one pound avoirdupois in troy measure? 3. Describe the process employed at the Exchequer for testing a given weight with the standard weight corresponding to it.

4. What is the object of enclosing the scales in a case?

5. What are the sources of error which it is necessary to guard against in making this test?

6. What is the standard measure of length in England?

7. How many square yards are there in a circle whose diameter is 3 ft. 6 in. ?

8. How many 3-inch cubes can be cut of a 12-inch cube?

9. What is the arrangement at the Exchequer for comparing measures of length with the standard?

10. What is the object of adopting a specified temperature at which these tests are to be made?

11. Suppose two brass rods were required to be compared together, what would be the effect as regards their corresponding lengths if the comparison was made at a temperature of 30 degrees below the standard temperature?

12. Suppose one brass rod was required to be compared with an iron rod, what would be the effect as regards their corresponding lengths at the standard temperature if the comparison were made at a temperature of 30 degrees below the standard temperature?

13. Name the measures of capacity for which standards exist at the Exchequer ?

14. What is the meaning of the term "specific gravity"?

15. If a square foot of iron one inch in thickness weighs 40.55 lbs., what is its specific gravity (assuming a cubic foot of water to weigh 1000 ounces)?

BOOK-KEEPING.

A paper similar to the following (A) or (B) is set to every Candidate who is examined in Book-keeping, along with a Special Paper adapted to the office for which he is a Candidate.

1. Copy the following transactions into the Sales Book and Invoice Book provided, putting all amounts for wine in the column headed Wine," and so with spirits and beer. All the details must be

given.

2. Post the transactions from these books into the Ledger, opening personal accounts only. The amount to be posted is that in the total column, and no details are to be given in the Ledger. Each Ledger entry must therefore be in the words "To" or "By " "Wine," "Beer," Spirits," or "Sundries."

The folio column in the Sales Book and Invoice Book is to be supplied with figures referring to the page of the Ledger to which each item has been carried; and the corresponding column in the Ledger is to be supplied with figures referring to the page of the Sales Book or of the Invoice Book from which each entry has been brought.

[The Ledger is not to be balanced; and no index to the Ledger need be made.]