30. What amount of stock in a manufacturing establishment, at an advance of 6 per cent, could be purchased for $1200? 31. A quantity of damaged cloth was sold for $250, which was at a loss of 16 per cent. For what sum was the cloth purchased ? 32. The population of a city increased from 7850 to 11775 inhabitants, in one year. What was the percentum of increase during the year? x Let a represent the percentum of increase; then since the population increased 11775-7850-3925 inhabitants in one year, we shall have the proportion 100x7850: 3925; from which a will be found equal to 50 per cent. Or, let x represent the percentum of increase; then since 7850x 100 represents the amount of percentage on 7850. Then, we shall have the Equation 33. An agent receives $2030 to invest in merchandise-himself to retain a commission of 1 per cent on the amount of the purchase What is the sum to be invested? 34. A merchant wishes to effect an insurance on a stock of goods amounting to $3573, which shall cover both the value of the goods and the premium of insurance. What is the sum to be insured, allowing the rate to be per cent? Let x represent the sum; then 100 100-3:x:3573; which will give x=$3600. Or, let x represent the sum; then since 3 4 3x 400 represents the premium of insurance. Then, we shall have the following Equation: 35. What amount of stock in a Savings Bank, at an advance of 5 per cent, could be purchased for $4200? and what amount in another, at a discount of 5 per cent, could be purchased for $1995? 1st. Let x represent the amount; then 100 105 x : 4200; from which x will be found = $4000. 2d. Let x represent the amount; then 100 100-5: :x : 1995; from which we shall find x=$2100. 36. What principal would amount to $1000 in 5 rate of interest to be 6 per cent? Let x represent the principal; then years allowing the 37. What is the Formula for finding the principal which, at interest at r per cent, would amount to the sum a in t years? Let x represent the principal; then represents the interest for one year; and rx 100 38. What principal would amount to $2500, in 10 years; allowing the rate of interest to be 7 per cent? 39. At what rate per cent must $1000 be put on interest to amount to $1150 in 2 years and 6 months? Let x represent the rate per cent; then from which we shall find x=6 per cent. 40. What is the Formula for finding the rate per cent of interest at which the sum s would amount to the sum a in t years? Let x represent the rate per cent; then represents the interest for one year; and SX 100 |