LOSS AND GAIN. 165. Loss and Gain is a rule by which merchants discover the amount lost or gained in the purchase and sale of goods. It also instructs them how much to increase or diminish the price of their goods so as to make or lose so much per cent. EXAMPLES. 1. Bought a piece of cloth containing 75yd. at $5,25 per yard, and sold it at $5,75 per yard: how much was gained in the trade? 2. Bought a piece of calico containing 50yd. at 2s 6d per yard: what must it be sold for per yard to gain £1 Os 10d? 3. Bought a hogshead of brandy at $1,25 per gallon, and sold it for $78: was there a loss or gain? Ans. loss of $0,75. 4. A merchant purchased 3275 bushels of wheat for which he paid $3517,10, but finding it damaged is willing to lose 10 per cent: what must he sell it for per bushel? Ans. $0,96+. 5. A bought a piece of cotton containing 40 yards, at 6 cents per yard; he sold it for 7 cents per yard: how much did he gain? Ans. $0,60. 6. Bought a piece of cloth containing 75 yards for $375: what must it be sold for per yard, in order to gain $100? Ans.$6,33 per yard. 7. Bought a quantity of wine at $1,25 per gallon, but it proves to be bad and am obliged to sell it at 20 per cent less than I gave: how much must I sell it for per gallon? Ans. $1 per gall. 8. A farmer sells 125 bushels of corn for 75cts. per bushel; the purchaser sells it at an advance of 20 per cent: how much did he receive for the corn? Ans. $112,50. 9. A merchant buys one tun of wine for which he pays $725, and wishes to sell it by the hogshead at an advance of 15 per cent: what must he charge per hogshead ? Ans. $208,43+. 10. A merchant buys 158 yards of calico for which he pays 20 cents per yard; one-half is so damaged that he is obliged to sell it at a loss of 6 per cent; the remainder he sells at an advance of 19 per cent: how much did he gain? Ans. $2,05+. EQUATION OF PAYMENTS. § 166. I owe Mr. Wilson $2 to be paid in 6 months; $3 to be paid in 8 months; and $1 to be paid in 12 months. I wish to pay his entire dues at a single payment, to be made at such a time, that neither he nor I shall lose interest at what time must the payment be made? The method of finding the mean time of payment of several sums due at different times, is called Equation of Payments. Taking the example above. Int of $2 for 6mo. " of $3 for " of $1 for 12mo. $6 8mo. = int. of $1 for 12mo. 48 1 × 6=12 3× 8=24 48 The interest on all the sums, to the times of payment, is equal to the interest of $1 for 48 months. But 48 is equal to the sum of all the products which arise from multiplying each sum by the time at which it becomes due: hence, the sum of the products is equal to the time which would be necessary for $1 to produce the same interest as would be produced by all the sums. Now, if $1 will produce a certain interest in 48 months, in what time will $6 (or the sum of the payments) produce the same interest. The time is obviously found by dividing 48, (the sum of the products), by $6, (the sum of the payments). Hence, we have the following RULE. Multiply each payment by the time before it becomes due, and divide the sum of the products by the sum of the payments: the quotient will be the mean time. 2. Bowes A $600: $200 is to be paid in two months, $200 in four months, and $200 in six months: what is the mean time for the payment of the whole? 3. A merchant owes $600, of which $100 is to be paid in 4 months, $200 in 10 months, and the remainder in 16 months if he pays the whole at once, at what time must he make the payment? Ans. 12 months. 4. A merchant owes $600 to be paid in 12 months, $800 to be paid in 6 months, and $900 to be paid in 9 months what is the equated time of payment. Ans. 8mo. 22da. 5. A owes B $600; one-third is to be paid in 6 months, one-fourth in 8 months, and the remainder in 12 months: what is the mean time of payment? Ans. 9 months. 6. A merchant has due him $300 to be paid in 60 days, $500 to be paid in 120 days, and $750 to be paid in 180 days: what is the equated time for the payment of the whole? Ans. 137 days. 7. A merchant has due him $1500; one-sixth is to be paid in 2 months; one-third in 3 months; and the rest in 6 months: what is the equated time for the payment of the whole? Ans. 4 months. NOTE. If one of the payments is due on the day from which the equated time is reckoned, its corresponding product will be nothing, but the payment must still be added in finding the sum of the payments. 8. I owe $1000 to be paid on the 1st of January, $1500 on the 1st of February, $3000 on 1st of March, and $4000 on the 15th of April: reckoning from the 1st of January, and calling February 28 days, on what day must the money be paid? Ans. Payment in 6714 days, or on the 8th March. Q. What is Equation of Payments? What is the sum of the products which arise from multiplying each payment by the time to which it becomes due equal to? How do you find the time of mean payment? When you reckon the time from the date at which the first first payment becomes due, do you include the first payment? FELLOWSHIP. § 167. Fellowship is the joining together of several persons in trade with an agreement to share the losses and profits according to the amount which each one puts into the partnership. The money employed is called the Capital Stock. The gain or loss to be shared is called the Dividend. It is plain that the whole stock which suffers the gain or loss must be to gain or loss, as the stock of any individual to his part of the gain or loss. Hence, we have the following As the whole stock is man's share to his share RULE. to the whole gain or loss, so is each of the gain or loss. Q. What is Fellowship? What is the gain or loss called? What is the rule for finding each one's share? EXAMPLES. 1. A and B buy certain merchandise amounting to £160, of which A pays £90, and B £70: they gain by the purchase £32: what is each one's share of the profits? 2. A and B have a joint stock of $2100, of which A owns $1800 and B $300: they gain in a year $1000: what is each one's share of the profits? Ans. A's $857,14+; B's=$142,85+. 3. A, B, C and D have £20,000 in trade: at the end of a year their profits amount to £16,000: what is each one's share, supposing A to receive £50 and D £30 out of the profits for extra services? A's £4030; B's=£3980; Ans. C's £3980; D's = £4010. 4. Five persons, A, B, C, D and E have to share between them an estate of $10,000: A is to have onefourth; B one-eighth; C one-sixth; D one-eighth; and E what is left: what will be the share of each? Ans. A's $2500; B's $1250; C's $1666,66+; D's $1250; E's $3333,34. PROOF. Add all the separate profits or shares together; their sum should be equal to the gross profit or stock. |