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storm they were obliged to cast 150 tons overboard. What loss does each sustain ?
See Part 1. Art. XVI., example 158 and following.
86. A father dying, bequeathed an estate of $12000 as follows: 1 to his wife, s to his eldest son, 1 to his second son, and } to his daughter. It is required to divide the estate in these proportions.
Note. Reduce the fractions to a common denominator, and the numerators will show the proportions.
87. Two men hired a pasture for $37, A put in 3 horses for 4 months, and B 5 horses for 3 months. What ought each to pay ?
Note. 3 horses for 4 months is the same as 4 times 3 or 12 horses for 1 month ; and 5 horses for 3 months, is the same as 3 times 5, or 15 horses for 1 month. The question therefore is the same, as if A had put in 12 horses and B 15. A must pay it and B , or, reducing the fractions, and so
88. Two men, A and B, traded in company : A put in $350 for 8 months, and B $640 for 5 months; they gained $250. What was the share of each ?
Note. Make the time equal, as in the last example.
89. Four men jointly hired a pasture for 20 English guineas ; A turned in 7 oxen for 13 days, B 9 oxen for 14 days, C 11 oxen for 25 days, and D 15 oxen for 37 days. How much ought each to pay !
90. A family of 10 persons took a large house for of a year, for which they were to pay $500, for that time. At the end of 14 weeks they took in 4 new lodgers; and after 3 weeks, 4 more ; and so on for every 3 weeks, during the term, they took in 4 more lodgers. What must one of each class pay per week of the rent ?
91. Three men enter into partnership and trade as follows: A put in 150£., and at the end of 7 months took out 50£. ; 5 months after he put in 170£ ;-B put in 205£., and at the end of 5 months, 110£. more, but took out 150£. 4 months after ;-C put in 300 guineas, at 28s. each, and when 8 months had elapsed, he drew out 150£., but 5 months after he put in 500£. Their partnership continued 18 months, at the end of which time they had gained 450.£ Required each person's share of the gain.
92. The last five are examples of compound or double fellowship. What rule can you make for it?
93. In how long time will 1 dollar gain as much interest as $15 will gain in 1 month ?
94. In how long time will 1 dollar gain as much interest as 8 dollars will gain in 3 months ?
95. In how long time will 1 dollar gain as much interest as 24 dollars will gain in 5 months ?
96. In how long time will 1 dollar gain as much interest as $158 will gain in 11 months ?
97. In how long time will 3 dollars gain as much interest as 1 dollar will gain in 24 months ?
98. In how long time will 28 dollars gain as much interest as 1 dollar will gain in 157 months ?
99. A lent B 8 dollars for 2 months, afterwards B lent A 1 dollar ; how long ought he to keep it to satisfy him for the former favour ?
100. C lent D 1 dollar for 15 months ; afterwards D lent C5 dollars ; how long ought he to keep it to satisfy him for the former favour ?
101. A borrowed of B 17 dollars for 11 months, promising him a like kindness ; afterwards B lent A 25 dollars. How long ought he to keep it?
Note. Find how long he ought to keep 1 dollar, and then how .ong he ought to keep 25 dollars.
102. I lent a friend 257 dollars, which he kept 15 months, promising to do me a like kindness, but he was not able to let me have more than 100 dollars; how long ought I to keep it?
103. A owes B notes to be paid as follows: 7 dollars to be paid in 3 months, and 5 dollars to be paid in 8 months ; but he wishes to pay the whole at once. In what time ought he to pay it ?
Note. 7 dollars for 3 months is the same as 1 dollar for 21 months; and 5 dollars for 8 months is the same as 1 dol. lar for 40 months. 40 + 21 = 61, and 7 +5= 12. He might have 1 dollar 61 months; the question now is how long he may keep 12 dollars. It is evident he might keep it 1 of 61 months.
104. C owes D $380, to be paid as follows ; $100 in 6 months; $120 in 7 months; and $160 in 10 months. He
wishes to pay the whole at once. In how long a time ought he to pay it ?
105. A merchant has due to him 300€. to be paid as follows; 50£. in 2 months ; 100£ in 5 months; and the rest in 8 months. It is agreed to make one payment of the whole. In what time ought he to receive it?
106. F owes H $1000, of which $200 is to be paid present, $400 in 5 months, and the rest in 15 months. They agree to make one payment of the whole. Required the time ?
107. A merchant has due a certain sum of mɔney, of which į is to be paid in 2 months, j in 3 months, and the rest in 6 months. In what time ought he to receive the whole ?
108. A merchant has three notes due to him as follows: one of $300 due in 2 months ; one of $250 due in 5 months; and one of $180 due 3 months ago; the whole of which he wishes to receive now. What ought he to receive, allowing 6 per cent. interest ?
Note. First find the equated time, and then the interest or discount for present payment, as shall be found necessary.
$300 for 2 months 1 dol. for 600 months.
1850 The two notes not yet due are the same as 1 dollar for 1850 months. But he has had $180 3 months after it was due, which is the same as 1 dollar for 540 months. This must be taken out of the other, and there will remain 1 dollar for 1310 months. If he can have 1 dollar for 1310 months, how long can he have $730 ?
1.8 nearly = 1 month and 24 daye :
584 As it is not due until I month and 24 days after this time, it must be discounted for that time. See Part 1. Art. XXIV., example 130 and following. 6 per cent for I year is 1 per cent. or .009 for 1 month and 24 days. The fraction then is 102. $730 is 108 of what?
109. A gave B four notes as follows; one of $75, dated 5th June, 1819, to be paid in 4 months; one of $150, dated 15th August, to be paid in 6 months ; one of $170, dated 11th September, to be paid in 5 months; and one of $300 dated 15th November, to be paid in 3 months. They were all without interest until they were due. On 1st January, 1820, he proposed to pay the whole. What ought he to pay?
110. A owes B $158.33, due in 11 months and 17 days, without interest, which he proposes to pay at present. What ought he to pay, when the rate of money is 5 per cent. ?
Note. The rate per cent. for 11 mo. 17 days, at 5 per cent. a year, is about 4% per cent. or .048, consequently the amount of 1 doll. is $1.048. $158.33 is 1865 of the num ber.
It is easy to find the rate per cent. of the discount for any given time, when the rate of interest is given. When interest is 6 per cent., that is, too, the discount is oo, because the discount of 106 dolls. is 6 dolls. If _6 be converted into a decimal, it gives the rate of discount in decimals, so that it may be computed in the same manner as interest.
This changed to a decimal is .0566. .057 — is sufficiently exact. This is 50 per cent. The rate must be found for the time required, before it is cs anged to a decimal.
In the last example the fraction would be 101, which is .046 nearly. Multiply the sum by this, and you will have the discount, which subtracted from the sum, will be the answer required.
111. What is the discount of $143.87 for 1 year and 5 months, when interest is 6 per cent. ?
112. What is the present worth of a note of $84.67, due in 1 year, 3 months, and 14 days, without interest, when the rate of interest is 5 per cent. ?
113. A man has a note of $647 due in 2 years and 7 months, without interest ; but being in want of the money,
he sells the note ; what ought he to receive, when the usual rate of interest is 6 per cent. ?
114. A gentleman divided $50 between two men, A and B. A's share was of B's. What was the share of each ?
Note. This question is to divide the number 50 into two parts, that shall be in the proportion of 3 and 7; that is, one
shall have 3 as often as the other shall have 7. 7 + 3 = 10. A had is and B ió
115. A gentleman bequeathed an estate of $12500 between his wife and son. The son's share was [ of the share of the wife. What was the share of each ?
116. What is the hour of the day, when the time past from midnight is equal to
of the time to noon ? 117. Two men talking of their ages, one says į of my age is equal to of yours : and the sum of our ages is 95. What were their ages ?
Note. To find the proportions, reduce them to a common denominator and take the numerators.
118. If a man can do of a piece of work in one day, in what part of a day can he do į of it? How long will it take him to do the whole ?
119. A farmer hired two men to mow a field ; one of them could mow of it in a day, and the other ş of it. What part of it would they both together do in a day? How long would it take them both to mow it ?
120. A gentleman hired 3 men to build a wall; the first could do it alone in 8 days, the second in 10 days, and the third in 12 days. What part of it could each do in a day? How long would it take them together to finish it? 121. A man and his wife tohto
they were together, a bushel of corn would last 15 days, but when the man was absent, it would last the woman alone 27 days. What part of it did both together consume in 1 day?
What part did the woman alone consume ? What part did the man alone consume ? How long would it last the man alone ?
122. Three men lived together, one of them found he could drink a barrel of cider alone in 4 weeks, the second could drink it alone in 6 weeks, and the third in 7 weeks. How long would it last the three together ?.
123. X cistern has 3 cocks to fill it, and one to empty it. One cock will fill it alone in 3 hours, the second in 5 hours, and the third in 9 hours. The other will empty it in my hours. If all the cocks are allowed to run together, in what time will it be filled ?
124. Divide 25 apples between two persons, so as to give one 7 more than the other.