Examples in Algebra for Senior Classes: Comprising Numerous Graduated Examples in Fractions, Surds Equations, Progressions, &c., with the Examination Papers for Civil Serive, Staff, and Artillery Appointments, College of Preceptors, London University, and Oxford and Cambridge Middle Class Examinations


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Σελίδα 70 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished four times as many men as there were companies in the...
Σελίδα 76 - There was a cask containing 20 gallons of brandy ; a certain quantity of this was drawn off into another cask of equal size, and this last filled with water, and afterwards the first cask was filled with the mixture. It now appears that if 6§ gallons of the mixture be drawn off from the first into the second cask, there will be equal quantities of brandy in each.
Σελίδα 70 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.
Σελίδα 78 - The fore wheel of a carriage makes 6 revolutions more than the hind wheel in going 120 yards ; but if the periphery of each wheel be increased one yard, it will make only 4 revolutions more than the hind wheel in the same space. Required the circumference of each.
Σελίδα 72 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.
Σελίδα 79 - The number of deaths in a besieged garrison amounted to 6 daily ; and allowing for this diminution, their stock of provisions was sufficient to last 8 days. But on the evening of the sixth day, 100 men were killed in a sally, and afterwards the mortality increased to 10 daily. Supposing the...
Σελίδα 62 - ... of their loads, which were in the ratio of 6 to 7, being taken out, their weights were then found to be in the ratio of 2 to 3, and the sum of their weights was then 10 tons; what were their weights at first? Ans. 16 and 20 tons.
Σελίδα 69 - There is a field in the form of a rectangular parallelogram, whose length exceeds the breadth by 16 yards; and it contains 960 square yards. Required the length and breadth. Ans. 40, and 24 yards. 4. A person being asked his age, answered, If you add the .square root of it to half of it, and subtract 12, there will remain nothing.
Σελίδα 86 - Find two numbers such that their sum shall be equal to the sum of their squares.
Σελίδα 61 - There is a cistern, into which water is admitted by three cocks, two of which are of exactly the same dimensions. When they are all open, five-twelfths of the cistern is filled in 4 hours ; and if one of the equal cocks be stopped, seven-ninths of the cistern is filled in 10 hours and 40 minutes : in how many hours would each cock fill the cistern ? Ans. Each of the equal ones in 32 hours, and the other in 24.

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