at an advanced price of 28. per yard, and gained by the whole £3. What were the lengths of the pieces? Ans. 17 yards the first, and 13 the second. 2. A bill of £26. 5s. was paid with half guineas and crowns, and twice the number of half guineas exceeded three times the number of crowns by 17. How many were there of each? Ans. 40 half guineas, and 21 crowns. 3. Two labourers, A and B, received £5. 178. for their wages; A having been employed 15, and B 14 days; and A received for working four days 118. more than B did for three days. What were their daily wages? Ans. A had 5s., and B 3s. a day. 4. A person had two casks, the larger of which he filled with ale, and the smaller with cyder. Ale being half a crown, and cyder 118. per gallon, he paid £8. 68.; but had he filled the larger with cyder, and the smaller with ale, he would have paid £11. 58. 6d. How many gallons did each hold? Ans. The larger contained 18, and the smaller 11 gallons. 5. A person expends half a crown in apples and pears, buying his apples at 4, and his pears at 5 a penny; and afterwards accommodates his neighbour with half his apples and one-third of his pears for 13 pence. How many did he buy of each? Ans. 72 apples, and 60 pears. 6. Two persons, A and B, played cards, each with a different sum. After a certain number of games, A had won half as much as he had at first, and found that if he had 158. more, he would have had just three times as much as B. But B afterwards won 10s. back, and he had then twice as much as A. What had each at first? Ans. A had 14, and B 19 shillings. 7. A certain sum of money put out to interest, amounts in 8 months to £297. 128.; and in 15 months its amount is £306 at simple interest. What is the sum, and the rate per cent.? Ans. £288, at 5 per cent. 8. A Farmer being asked how many quarters of wheat he had sold in the market, answered, if he had sold 8 quarters more, and got 7s. per quarter more than he did, he should have received £11. 158. more than he had: but if he had sold 7 quarters more at ss. per quarter more, he should have had £11. 178. more. How many quarters did he sell, and what was the price? Ans. 13 quarters, at 118. per quarter. 9. There is a number consisting of two digits, the second of which is greater than the first; and if the number be divided by the sum of its digits, the quotient is 4; but if the digits be inverted, and that number divided by a number greater by 2 than the difference of the digits, the quotient becomes 14. quired the number. Ans. 48. Re 10. What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes 2 3 ; but the denominator being doubled, and the numerator increased by 2, the value becomes? 5 4 Ans. 11. A Farmer parting with his stock, sells to one person 9 horses and 7 cows for £300; and to another, at the same prices, 6 horses and 13 cows for the same sum. What was the price of each? Ans. The price of a cow was £12, and of a horse £24. 12. A Farmer hires a farm for £245 per ann., the arable land being valued at £2 an acre, and the pasture at 28 shillings; now the number of acres of arable is to half the excess of the How many acres were there arable above the pasture as 28: 9. of each? Ans. 98 acres of arable, and 35 of pasture. 13. A person owes a certain sum to two creditors. At one time he pays them £53, giving to one four-elevenths of the sum which is due, and to the other £3 more than one-sixth of his debt to him. At a second time he pays them £42, giving to the first three-sevenths of what remains due to him, and to the other one-third of what is due to him. What were the debts? Ans. £121, and £36. 14. A and B playing at backgammon, A bet 3s. to 28. on every game, and after a certain number of games found that he had lost 17 shillings. Now had A won 3 more from B, the number he would then have won, would have been to the number B would have won as 5 to 4. How many games did they play ? Ans. 9. 15. A Vintner has 2 casks of wine, from the greater of which he draws 15 gallons, and from the less 11; and finds the quantities remaining in the proportion of 8 to 3. they become half empty, he puts 10 gallons of water into After each, and finds that the quantities of liquor now in them are as 9 to 5. How many gallons will each hold ? Ans. The larger 79, and the smaller 35 gallons. 16. A person having laid out a rectangular bowling-green, observed that if each side had been 4 yards longer, the adjacent sides would have been in the ratio of 5 to 4; but if each had been 4 yards shorter, the ratio would have been 4 to 3. What are the lengths of the sides? Ans. 36, and 28 yards. 17. At an election for two members of parliament, three men offer themselves as candidates, and all the electors give single votes. The numbers of voters for the two successful ones are in the ratio of 9 to 8; and if the first had had 7 more, his majority over the second would have been to the majority of the second over the third as 12:7. Now if the first and third had formed a coalition, and had one more voter, they would each have succeeded by a majority of 7. How many voted for each? Ans. 369, 328, and 300, respectively. 18. Determine three numbers such that if 6 be added to the first and second, the sums will be in the proportion of 2: 3; if 5 be added to the first and third, the sums will be in the proportion of 7:11; but if 36 be subtracted from the second and third, the remainders will be as 6: 7. 19. Ans. 30, 48, 50. Two shepherds, A and B, are intrusted with the charge of two flocks of sheep. A's consisting chiefly of ewes, many of which produced lambs, is at the end of the year increased by so; but B finds his stock diminished by 20; when their numbers are in the proportion of 8 to 3. Now had A lost 20 of his sheep, and B had an increase of 90, the numbers would have been in the proportion of 7 to 10. What were the numbers? Ans. A's 160, and B's 110. 20. Two persons, A and B, can perform a piece of work in 16 days. They work together for 4 days, when A being called off, B is left to finish it, which he does in 36 days more. what time would each do it separately? Ans. A in 24 days, and B in 48 days. In 21. There is a cistern, into which water is admitted by three cocks, two of which are exactly of the same dimensions. When they are all open, five-twelfths of the cistern is filled in four hours; and if one of the equal cocks be stopped, seven-ninths of the cistern is filled in ten hours and forty 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. 22. Some hours after a courier had been sent from A to B, which are 147 miles distant, a second was sent, who wished to overtake him just as he entered B; in order to which he found he must perform the journey in 28 hours less than the first did. Now the time in which the first travels 17 miles added to the time in which the second travels 56 miles is 13 hours and 40 minutes. How many miles does each go per hour? Ans. The first goes 3, and the second 7 miles an hour. 23. Two loaded waggons were weighed, and their weights were found to be in the ratio of 4 to 5. Parts of their loads, which were in the proportion 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 the weights at first? Ans. 16, and 20 tons. |