241. It may happen that the three given quantities are all of one denomination; nevertheless it will be found that two of them are of one, and the third of another sort. For example: What must an income of £400 pay towards an income-tax of 4_s._ 6_d._ in the pound? Here the three given quantities are, £400, 4_s._ 6_d._, and £1, which are all of the same species, viz. money. Nevertheless, the first and third are income; the second is a tax, and the answer is also a tax; and therefore, by (152), the quantities must be placed thus: £1 : £400 ∷ 4_s._ 6_d._ 242. The following exercises either depend directly upon this rule, or can be shewn to do so by a little consideration. There are many questions of the sort, which will require some exercise of ingenuity before the method of applying the rule can be found. EXERCISES. If 15 cwt. 2 qrs. cost £198. 15. 4, what does 1 qr. 22 lbs. cost? _Answer_, £5 . 14 . 5 ¾ ¹⁸⁵/₂₁₇. If a horse go 14 m. 3 fur. 27 yds. in 3ʰ 26ᵐ 12ˢ, how long will he be in going 23 miles? _Answer_, 5ʰ 29ᵐ 34ˢ(²⁴⁶²/₂₅₃₂₇). Two persons, A and B, are bankrupts, and owe exactly the same sum; A can pay 15_s._ 4½_d._ in the pound, and B only 7_s._ (6¾)_d._ At the same time A has in his possession £1304. 17 more than B; what do the debts of each amount to? _Answer_, £3340 . 8 . 3 ¾ ⁹/₂₅. For every (12½) acres which one country contains, a second contains (56¼). The second country contains 17,300 square miles. How much does the first contain? Again, for every 3 people in the first, there are 5 in the second; and there are in the first 27 people on every 20 acres. How many are there in each country?--_Answer_, The number of square miles in the first is 3844⁴/₉, and its population 3,321,600; and the population of the second is 5,536,000. If (42½) yds. of cloth, 18 in. wide, cost £59. 14. 2, how much will (118¼) yds. cost, if the width be 1 yd.? _Answer_, £332. 5. (2⁴/₁₇). If £9. 3. 6 last six weeks, how long will £100 last? _Answer_, (65¹⁴⁵/₃₆₇) weeks. How much sugar, worth (9¾d). a pound, must be given for 2 cwt. of tea, worth 10_d._ an ounce? _Answer_, 32 cwt. 3 qrs. 7 lbs. ³⁵/₃₉. 243. Suppose the following question asked: How long will it take 15 men to do that which 45 men can finish in 10 days? It is evident that one man would take 45 × 10, or 450 days, to do the same thing, and that 15 men would do it in one-fifteenth part of the time which it employs one man, that is, in (450 ÷ 15) or 30 days. By this and similar reasoning the following questions can be solved. EXERCISES. If 15 oxen eat an acre of grass in 12 days, how long will it take 26 oxen to eat 14 acres? _Answer_, (96¹²/₁₃) days. If 22 masons build a wall 5 feet high in 6 days, how long will it take 43 masons to build 10 feet? _Answer_, (6⁶/₄₃) days.