142. A herder has charge of 1140 sheep and goats, the number of sheep being 40% greater than the number of goats. How many sheep were in charge of the herder?

143. A firm expended $3456.60 per annum for advertisements; $4049.16 for wages; $1382.64 for store rent and insurance; and $987.60 for other expenses. What per cent. of the sum of these expenses was incurred for advertisements? For wages? For rent and insurance? For other expenses?

144. In the manufacture of cloth 1122 lb. of cotton and wool were mixed, the weight of the cotton being 30% of the weight of the wool. How many pounds of each did the mixture contain ?

145. The sum paid for two farms is $9310. If 80% of the sum paid for one farm is equal to 120% of the sum paid for the other, how much was paid for each?

REM.-Find what per cent. of either farm equals 100% of the other, and proceed as in Ex. 144.

146. A dealer purchased a quantity of oysters, fish, and clams, and paid for the entire quantity $166.75. The cost of the fish was 45% of that of the oysters, and the cost of the clams 25% of that of the oysters and fish together. What was the cost of each?

147. The sales of a firm were increased 25% the second year, 20% the third year, and 163% the fourth year. What was the amount of sales during the first year, if the fourth year's sales were $60248?

148. The population of a certain city decreased in 1882, 10%; and in 1883, 8%. On Jan. 1, 1884, the population was 26910. What was the population on Jan. 1, 1882 ?

149. An importer paid £243 15s. for an invoice of goods, and £73 2s. 6d. for freight, custom-house charges, etc. What per cent. of the invoice price were the charges?

150. The charge for a certain class of "through freight" between two cities, 400 miles distant from each other, was 95 cents per 100 pounds, and the quantity transported was 8600 pounds. The freight was divided pro rata between three railroad companies, whose mileage was respectively 120, 180, and 100 miles. What per cent. of the total freight should each company have received? What sum?

151. A has $276 and B $368. What per cent. of A's money is B's? 152. At the election of a U. S. Senator, the total number of votes

cast by a legislature was 120, and the successful candidate received a majority of 30% of the total votes cast. How many votes did he receive?

153. In the manufacture of a certain quality of blankets, 2380 pounds of cotton and wool were used, the quantity of wool being 140% greater than that of the cotton. What was the weight of the wool ?

154. A man withdrew 30% of his deposit from a bank, and invested 12% of what he withdrew in purchasing an organ for $180. How much had he remaining in the bank?

155. On December 18, 1883, a merchant bought a bill of goods amounting to $736.80 on 4 months' credit, or 5% off if paid within 30 days of date of sale. What sum will pay the bill on Jan. 5, 1884?

156. Two railroads, whose lengths were respectively 175 and 125 miles, transported 7500 pounds of merchandise at the "through rate" of 45 cents per 100 pounds. What per cent. of the total freight did each company receive? What sum ?

15%. If coffee loses 8% of its weight in roasting, how much green coffee will be required to produce 828 pounds when roasted?

158. If 80% of A's money equals 70% of B's, and 75% of B's equals 60% of C's, how much has each if 30% of C's is $240?

159. A merchant lost $5000 of his capital, and had $25000 remaining. What per cent. of his capital did he lose?

160. By purchasing improved machinery, a miller increased the capacity of his mill 25%, or 340 barrels of flour per month. What is the present capacity of the mill ?

161. A's money is 20% of B's and 30% of C's. How much money has A, if the difference between B's and C's is $125 ?

162. A is worth $18750, or 20% more than B and 25% less than C. What are B and C worth?

163. A paid B $262.50, or 35% of what he owed him. How much did A still owe B?

164. An army lost 4077 men in a certain battle, and after the battle numbered 41223 men. What % of the army was lost?

165. 18% of a man's wealth is in real estate, 24% in bank stock, 26% in railroad bonds, and the remainder in money. What is the value of his bank stock if his money amounts to $10288 ?

166. The foreign-born inhabitants of a certain city were 30% of the native-born. What % of the total population was each ?

167. A man started from home with $800.80 and returned with $715. What% of what he returned with did he pay out during his absence?

168. A grocer sold 153 pounds of coffee and had 27 pounds remaining. What per cent. of the coffee did he sell?

169. A gentleman paid $1701 in settlement of an account, and afterwards found that he had paid 26% more than the correct sum. was the amount of overcharge?

What

170. A and B invested equal sums in speculation, A losing 27% of his investment and B gaining 17%, or $1399.10. What was A's loss?

171. A dealer bought mackerel and herring at a total cost of $1898.65, paying 30% more for the mackerel than for the herring. What was the cost of each?

172. A man bought 273 barrels of flour at $7.50 per barrel, and made a partial payment thereon which was 30% of what he still owed. What was the amount of his payment?

173. A grain merchant bought a quantity of rye and, oats for $1860, and 30% of what he paid for the oats is 25% more than the sum paid for the rye. How many bushels of each did he buy, if the price of the rye was 90 cents per bushel, and of the oats 60 cents per bushel?

174. A and B had equal sums of money, but after A collected $1.66 and B spent $5.20, it was found that A's money was 35% greater than B's. How much had each at first?

175. A gentleman withdrew 20% of his bank deposit, expended 45% of what he withdrew in buying a tract of land, 7% of the remainder in enclosing the land, $475 of what was left in buying a pair of horses, and he re-deposited the unexpended balance, or $906.05, in bank. What sum had he then on deposit?

176. A has 15% less money than B. What per cent. more than A's money is B's?

177. If A has 25% more money than B, what per cent. of A's money is B's?

178. A merchant found that his sales in 1881 were 20% greater than his sales in 1880; in 1882, 30% greater than in 1881; in 1883, 25% greater than in 1882. If his sales in 1883 were $3600 greater than his sales in 1881, what were his sales in 1882?

179. A man bought a horse and buggy for $570, paying 28% more for the horse than for the buggy. What did he pay for each?

180. A bought 75 barrels of flour, and B increased his stock of flour 28% by buying 16% less than A. How many barrels did B have after his purchase?

181. I sold tea and sugar at a total gain of $7.54, the gain on sugar being 45% of the gain on tea. What was my gain on each?

182. A wool merchant's profits averaged $33.74 each day for one week. His gain on Tuesday was 163% more than on Monday; and his gain on Wednesday was 75% of his gain on Tuesday; on Thursday his profits were 50% of his gain on the first three days of the week; his gain on Friday was $32.10, and on Saturday his gain was equal to the gain on both Wednesday and Thursday together. What was each day's gain, except Friday's?

PROFIT AND LOSS.

INDUCTIVE EXERCISE.

1. If a coat cost $12, what should be the selling price to produce a gain of $3? To produce a loss of $3? How was each of the preceding selling prices obtained? If the selling price of a coat be $15, to what standard must it be compared to find whether it will produce a gain or a loss? Hence, what would you infer to be a rational basis for all computations involving profit or loss? Since all rates % express hundredths of a base [e, page 144], upon what base are all rates % of profit, loss, or selling price expressed? Since the cost is the base, and there is only one other concrete term of percentage, as what must all profits, losses, or selling prices be regarded [h, page 144]?

[a] The cost is the base.

[b] The profit, loss, and selling price are percentages.

[c] The rate of profit, of loss, or of selling price is the rate.

[d] The cost being the normal base in computing profit and loss, all rates per cent. are UNDERSTOOD to express hundredths of the cost.

[e] The terms of profit and loss have the same relation to each other as have the three terms of multiplication : the cost corresponding to the multiplicand; the rate of profit, of loss, or of selling price to the multiplier; and the profit, loss, or selling price to the product.

The cost and rate of profit or of loss being given, to find the profit, the loss, or the selling price.

INDUCTIVE EXERCISE.

1. With what term of percentage does the cost correspond? The rate of profit? The profit? Hence, with what term of multiplication does each correspond? If the cost [multiplicand] and the rate of profit [multiplier] are given, how may the profit [product] be found?

2. What is the gain on merchandise which cost $300, and is sold at 6% profit? At 8%? At 10%? At 12%? At 15%? At 20%? At 25% ?

3. What is the loss on merchandise which cost $400, and is sold at 5% loss? At 7%? At 9%? At 4%? At 11%? At 20%?

4. If the cost and profit are given, how is the selling price found? Hence, if the rate of cost [100%] and rate of profit are given, how is the rate of selling price found? If the rate of cost and rate of loss are given, how is the rate of selling price obtained, and why?

5. What is the rate % of selling price if the rate of profit is 5%? 9%? 12%? 35%? 42%? 45%? 50% ? If the rate of loss is 3%? 5%? 6%? 8%? 10%? 16%? 23%? 25%? 40%?

[f] Cost × rate of profit, loss, or selling price = profit, loss, or selling price.