It is plain that $20 is the amount made. What per cent is this of $200: that is, how many hundredths of 200? If we add two ciphers and divide, the quotient will express the hundredths: Thus, that is, 20 is ten per cent of 200. Hence, to determine the per cent which one number is of another, we have the following RULE. I. Bring the number to hundreds by annexing two ciphers or removing the decimal point two places to the right. II. Divide the number so formed by the sum on which the percentage is estimated: the quotient will express the per cent. 2. A man has $550 and purchases goods to the amount of $82,75: what per cent of his money does he expend? 3. A merchant goes to New-York with $1500; he first lays out 20 per cent, after which he expends $660: what per cent was his last purchase of the money that remained after his first? Ans. 55 per cent. 4. Out of a cask containing 300 gallons, 60 gallons is drawn what per cent is this? 5. If I pay $698,33 for 3 hogsheads of molasses and sell it for $837,996, how much do I gain per cent on the money laid out? Ans. 20 per cent. 6. If I pay $698,33 for 3 hogsheads of sugar and sell them for $837,996, how much do I make per cent on the amount received? 7. A man gave his note for $240, and soon after made a payment of $160: what per cent of the debt did he pay? Ans. 663 per cent. The per cent of loss or gain being given, and the amount received, to find the principal or cost. 1. I sell a parcel of goods for $170, by which I lose 15 per cent: what did they cost? It is evident that the cost, less 15 per cent, that is, less 15 hundreths of the cost, is equal to $170. Hence, 85 hundredths of the cost is equal to $170; and consequently, the cost is equal to $170x100÷85-$200 cost. Hence, to find the cost when there is a loss, Multiply the amount received by 100 and divide the product by the difference between 100 and the per cent. 2. Sold a parcel of goods for $195,50, on which I made 15 per cent: what did they cost me? It is evident that the cost added to 15 hundredths of the cost, will be equal to what the goods brought, viz, $195,50. If we call the cost 1, then 100 of the cost, plus 15 of the cost is equal to what they bring: That is of cost $195,50; or, cost equals $195,50×100÷115=$170. Hence, to find the cost when there is a gain, Multiply the amount by 100 and divide the product by 100 plus the per cent. 3. Sold cloth at $1,25 per yard and lost 15 per cent: For what should I have sold it to gain 12 per cent? Ans. $1,647019 per yard. 4. Sold cloth at $1,25 per yard and lost 15 per cent: what per cent should I have gained had I sold it at $1,647019 per yard? 5. Sold cloth at $1,647019 per yard and gained 12 per cent: for what ought I to have sold it to lose 15 per Ans. $1,25 per yard. cent? INSURANCE. 1. What is the premium of insurance on $9870, at 14 per cent? Ans. $1381,80. 2. A merchant wishes to insure on a vessel and cargo at sea, valued at $28800: what will be the premium a 12 per cent? 3. What is the premium on $750 at 12 per cent? Ans. $13,121. 4. What is the premium of $8750 at 3 per cent? 5. A merchant owns three-fourths of a ship valued at $24000, and insures his interest at 2 per cent: what does he pay for his policy? Ans. $450. 6. A merchant learns that his vessel and cargo valued at $36000, have been injured to the amount of $12000; he effects an insurance on the remainder at 5 per cent: what premium does he pay? 7. What is the insurance on my house valued at 5000 at per cent? Ans. $12,50. BANKING. When a bank discounts a note, it is customary to subtract from the face of the note the interest for the time which must elapse before the note becomes due; and the difference between this sum and the face of the note, is what the bank credits as the value of the note. A person is not obliged to pay a note until three days after it falls due. These are called days of grace. The bank, that it may lose no interest, always charges interest for the days of grace. Thus, if a note is made payable in thirty days, a bank which discounts it will charge interest for thirtythree days. 1. What is the bank discount of a note of $1000 payable in 60 days, at 6 per cent interest? Ans. $10,49 9+. 2. A merchant sold a cargo of cotton for $7860 for which he receives a note at 6 months: how much money will he receive at a bank for this note, discounting it at 6 per cent interest? 3. What is the bank discount on a note of $100 payable in 60 days, discounted at 6 per cent per annum? Ans. $1,04 9+. 4. A has a note against B for $1728, payable in three months; he gets it discounted at 6 per cent interest: how much does he receive? LOSS AND GAIN. 1. If I buy coffee at 16 cents and sell it at 20 cents: how much do I make per cent on the money paid? Ans. 25 per cent. 2. If I buy tea at 4s per pound and sell it at 4s 9d per pound: how much should I gain on a purchase of £100? 3. A merchant bought 650 pounds of cheese at 10 cents per pound, and sold it at 12 cents per pound: how much did he gain on the whole, and how much per cent on the money laid out? Ans. {gain 20 per cent. 4. Bought cloth at $1,25 per yard, which proving bad, I wish to sell it at a loss of 18 per cent: how much must I ask per yard? 5. Bought 50 gallons of molasses at 75 cents a gallon, 10 gallons of which leaked out. At what price per gallon must the remainder be sold that I may clear 10 per cent on the cost? Ans. $1,0311. 6. Bought a cow for $30 cash, and sold her for $35 at a credit of 8 months: reckoning the interest at 6 per cent how much did I gain? 7. Bought 67 yards of cloth for $112, but 19 yards being spoiled, I am willing to lose 5 per cent: how much must I sell it for per yard? Ans. $2,2163. 8. Bought 67 yards of cloth for $112, but a number of yards being spoiled, I sell the remainder at $2,2163 per yard, and lose 5 per cent: how many yards were spoiled? FELLOWSHIP. 1. A bankrupt is indebted $2729, viz: to A $500,37; to B $228; to C $1291,23; and to D $709,40; but his estate is only worth $2046,75. How much can he pay on the dollar, and how much will each creditor receive? 75 cents on the dollar; A gets $375,273; Ans. B $171; C $968,421; and D $532,05. 2. A, B, and C send a ship to sea, which together with her cargo was worth $15000. A and B owned each onefifth, and C the rest. They gained $1250: how much did each pay towards the ship and cargo, and what did each receive of the profits? 3. A man bequeathed his estate to his four sons in the following manner, viz: to his first $5000; to his second $4500; to his third $4500; and to his fourth $4000. But on settling his estate it was found that after paying debts, charges, &c. only $12000 remained to be divided: how much must each receive? Ans. Sfirst son $3333,331; second $3000; third $3000; fourth $2666,663. 4. A widow and her two sons have a legacy of $1500, of which the widow is to have one-half and the son's each one-fourth. Now suppose the eldest son to relinquish his share, and the whole to be divided in the above proportions between the mother and younger son, what will each receive? 5. Suppose premiums to the value of $12 are to be distributed in a school in the following manner. The premiums are divided into three grades. The value of a premium of the first grade is twice the value of one of the second; and the value of one of the second grade twice that of the third. Now there are 6 to receive premiums of the first grade, 12 of the second, and 6 of the third: what will be the value of a single premium of each grade? (1st grade $0,888. $0,44. Ans. 2d 66 $0,223. 6. Four traders form a company: A puts in $400 for 5 months; B $600 for 7 months; C $960 for 8 months; D $1200 for 9 months. In the course of trade they lost $750: how much falls to the share of each ? 7. A and B lay out certain sums in merchandise amounting to $320, of which A pays $180 and B $140; they gain by the purchase $64: what is each one's share? Ans. A's $36; B's $28. |