8. A man allows to his agent 5 per cent. on his gross in 1 come for the expense of collecting his rents. He spends th of his net income in assuring his life, and this part of his income is in consequence exempt from income-tax. The income-tax being 10d. in the pound, and his income-tax amounting to £38, 198.; find his gross income. 9. A young lady desires to paper her room with postage stamps, but being herself unable to calculate the number which will be required, she supplies the following data: her room is 14 ft.,, 9 in. long, 9 ft.,, 3 in. broad, and 10 ft. „,6 in. high; it contains two windows, each 51 ft. by 4 ft., and 3 doors, each 6 ft. by 3 ft.; a postage stamp is 3 in. broad. Make the calculation for her. 4 15 3 360, area of 4 walls 6 46, area of doors 82, area to be deducted 29 t, area to be papered 12 33 12 406, square feet to be papered. But X is the fraction of a square inch covered by each 16 4 10. The area of the coal field of South Wales is 1000 square If the coal annually consumed in this country were piled N.B. The volume of a pyramid is equal to the area of Each square mile contains 1760 × 1760 square yards; and as the thickness of the coal is 20 yards, the content of coal field is 1000 × 1760 × 1760 × 20 cubic yards, and this weighs 1000 × 1760 × 1760 x 20 tons. Also, volume of required pyramid is 70,000,000 cub. yds. 11. Define discount and present worth. Find the present worth of a bill of £283,, 10s. due 41 months hence at 3 per cent. Distinguish between the mathematical and the mercantile discount, and find their difference in the above example. But the mercantile discount is only the simple interest on 12. A man invests £4297 „, 10s. in the 3 per cents. at 951⁄2. He sells out one-third of his stock when the funds have fallen to 94, £1600 stock when they have risen to 961, and the remainder at par. What sum does he gain? And, if he invests the proceeds in the French 3 per cents. at 67.50, what is the difference in his income? And as he held this stock in the 3 per cents., the income he obtained was £135. Now one-third of this, or 1500 is sold out at 94, 1600 at 961, 1400 at 100. Therefore he receives 15 × 94 +16 × 961 +1400, or 1410+1540 +1400, or 4350 cash. Therefore the sum he gains is £52,, 10s. By investing in the French 3 per cents., we have 67.5: 4350 :: 3 : Ans. DD therefore £193,, 68. „, 8d. – 135 = £58, 68. „, 8d., the gain in his income. First Division B, 1860. 1. Explain the common system of notation and point out its advantages. From 613 take 49 explaining the reasons for the process. 2. Define a vulgar fraction, and shew that a fraction is not altered in value if the numerator and denominator be multiplied by the same quantity. In what operations on fractions is this change necessary? A has three times as much money as B. They play together for a stake, and at the end of the 1st game B wins from A ths of A's money. What frac 3 8 tion of the sum B now has must A win back in the second game, that they may have exactly equal sums ? 3. Define a decimal fraction, and taking 7256 as an exam ple, shew from your definition that·7256 = 3 8 35 7256 10000 and and the sum, and the pro108, 4. Express of 7s. „, 6d. +625 of 10s.-545 of 9s. „, 2d. as a 6. A farmer rents a farm of 800 acres on the following terms He pays a fixed rent of 48. 6d. per acre, and a corn rent of 250 quarters of wheat, 150 quarters of barley, and 100 quarters of oats. The price of wheat, barley, and oats being respectively 45s., 29s. „ 4d. and 19s.,, 6d. per quarter, find his rent per acre. |