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Ratio, , The ratio between two quantities is the quotient obtained by dividing the first quantity by the second. For, example, the ratio between 3 and 12 is and the ratio between 12 and 3 is 4. ratio is generally indicated by, , the sign ‘:’, Thus, 12:3 indicates the ration of 12 to 3., , A reciprocal or inverse ratio is the reciprocal of the original ratio. Thus the inverses ratio of 5:7 is 7: 5., , The first term of a ratio is called antecedent and the second term is called consequent., , Proportion:, , Proportion is the equality of ratios, Thus,, , 6:3 = 10:5 or 6:3 :: 10:5, , The first and last terms is a proportion are called the extremes; the second and third, the means. The product, , of the extremes is equal to the product of the means., , Thus, 6:3 = 10:5 and6x5=3x10, , Mixture and allegation:, Allegation is the rule that enables us to, i. find the mean or average value of a mixture., , ii. find the proportion of the mixture., , Tips:, Cc wi 7, a —, [Dear - Mean] [Mean - Cheap], , Taking only the absolute value, , * Mean = Cost price of the mixture, Final concentration of the mixture, , * The first entity should always be on the left side., , Example:, , In what proportion must a grocer mix two teas, one priced tk. 1.25/ kg and the other tk. 1.50/ kg , so that the, mixture may be worth tk. 1.30/ kg?

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Solution: here, Cheap = 1.25, Dear = 1.50, Mean = 1.30, , Ratio = 0.20: 0.05, = 20:5, = 4:1, , wes, a, 4 1.30 NQ, 0.20 0.05, , Formula:, , Cy Chg oer ceiscrrsy sercteiers (Og FO H ccceerarn en VE, , Here, Q, = Quantity of first mixture, , C, = Price / concentration of first mixture, Q2 = Quantity of second mixture, , C> = Price / concentration of second mixture, , C = Final price / concentration, , Example:, A mixture of milk and water weighting 5 kg contains 5% water. How much more water must be poured into, , it to make it 10%?, , here, water’s concentration in first mixture, C; = 5%, , water’s concentration in second mixture, C, = 100%, [Only water will be poured, so water’s concentration 100%], quantity of first mixture, Q,= 5 kg, , let, quantity of second mixture Q, =, , final concentration, C = 10%

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Now,, , QiC, + Q2Cz = C(Q; + Qz), >5x5+xx100 = 10(5+x), => 25+ 100x = 50+ 10x, , ssi gs Ma, 9. 18°©, 5, + Q, =akg, Formula:, , Suppose a container contain x units of liquid from which y units are taken out and replaced by water. After n, , , . — y\*, operation, the quantity of pure liquid = [x (1 _ 4) units., , Example:, 8 liters are drawn from a cask full of wine and then filled with water. This operation is performed three more, , times. The ratio of the quantity of wine now left in cask to that of the water in 16:65. How much wine did, , the cask hold originally?, A. 18 liters B. 24 liters C. 32 liters D. 42 liters E. None of these, , Solution:, , Let, the quantity of the wine in the cask originally be x liters. Then, the quantity of the wine left in cask after, , 4, 4 operations = [x (1 = =) liters, , 4, x(1-3) _16, x 81, (:-9'-@, # 3, => 3x -—24=2x, >x=24, , Practice Test, 1. Two number are in the ratio 5: 4 and their difference is 10. What is the largest number?, , A. 40 B. 30 C. 50 D. 45 E. 55, , 2. If 20% A = 30% of B = of C, Then A: B:C is?, , A. 2:3:16 B: 3:2: 16 GC, 10; 18: 18 D. 15:10:18 E. None of these

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3. 35% of Nadias income is equal to 25% of Nurus income. The ratio of their income is —, , A225 Bn TS CaF D. 7:3 BE. 3:7, , 4. If a and b are integer greater than 100 such that a + b = 300, which of the following could be the exact, , ratio of a to b? [BBA 15-16], A. 9to 1 B. 5 to 2 C563 D. 4to 1 E.3 to2, , . 4 ,, 5. Two container x and y of the same capacity, are each 7 full of water. If 4 liters of water from container x, , is added to container y, the ratio of water is the two containers becomes 2:3. What is the capacity of, , container x? [BBA 14-15], A. 16 B. 20 C. 25 D.:32 E. None of these, , 6. The current ratio of boys to girls at a certain school is 2 to 5. If 12 additional boys were added to the, , school, the new ratio of boys to girls would be 4 to 5. How many boys do currently attend the school?, , A. 27 B. 54 C. %2 D. Cannot be determined E. None of these, , 7. In a mixture of 50 liters milk and water are in the ratio of 3:2. How much water would be added to the, , mixture to make the ratio of the two equal?, , A. 14 liters B. 12 liters C. 10 liters D. 8 liters E. None of these, , 8. A drink contains 20% cranberry juice 20%, raspberry juice and the rest is apple juice. You added 250 ml, of water to 750 ml of the drink. Now what is the ratio of water to apple juice in the drink? [BBA 15-16], A. 6:5 B. 9:5 C.342 D. 5:9 E. None of these, , 9. Two equal glasses are respectively one third and one fourth full of milk. They are then filled up with, , water and the contents are mixed in a tumbler. Ratio of milk and water in tumbler is:, , A: TiS B. 7: 17 C357 D. Liszs E. None of these, , 10. Solution X contains 7% (by weight) of liquid M and solution Y contain 14.5% (by weight) of liquid M., If 3 grams of solution X is mixed with 2 gram of solution Y, then liquid M accounts for what percent of the, , weight of the resulting solution?, , A. 6.09% B. 10% C. 10.75% D. 21.5% E. None of these, , 11. In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3:, 2 respectively. The number of girls not participating sin the sports is 5 more than the number of boys not, participating in the sports. If the number of boys participating in the sports is 15, then how many girls are, , there in the class:, A. 20 B. 30 G2 D. 35 E. None of these

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12. The ratio of the number of plants that Kishore has to the number of plants Saad has is 1:5. After Saad, , gives Kishore 5 plants, the ratio of plants Kishore has to the plants Saad has will be 2:7. How many more, , plants will Saad have than Kishore after 5 plants are given?, , A. 30 B. 45 C. 50 D. 60 a, , 13. The ratio of flour to water to sugar in a receipe is 7: 4: 1. The ratio in a new receipe calls for a doubling, of the ratio of flour to water from the original receipe and a halving of the ratio of flour to sugar. If the new, , receipe calls for 8 cups of water, how much sugar is required?, , A. 4 cups B. 6 cups C. 8 cups D. 12 cups E. 16 cups, , 14. A milk vender contains 2 cans of milk. The first contains 25% water and the rest milk. The second, contains 50% water. How much milk should he mix from each of the containers so as to get 12 liters of milk, , such that the ratio of water to milk is 3:5?, , A. 4 liters, 8 liters B. 6 liters, 6 liters C. 5 liters, 7 liters D. 7 liters, 5 liters E. 8 liters, 4 liters, , 15. Sixty percent of the rats included in an experiment were female rats. If some of the rats died during an, experiment and 70 percent of the rats that died were male rats, what was the ratio of the death rate among, , the male rats to the death rates among the female rats?, , A. 7:2 B. 7:3 G27 D. 3:7 E. Cannot be determined, , 16. The vessels contain water and milk in the ratio 1:2 and 2:5 are mixed in the ratio 1:4. The resulting, , mixture will have water and milk in the ratio?, , A. 31:74 B. 31:75 C. 30:77 D. 30:74 E. 31:77, , 17. A sample of x liters from container having a 60 liter mixture of milk and water in the ratio of 2:3 is, replaced with pure milk so that the container will have milk and water in equal proportions, what is the value, , of x?, , A. 6 liters B. 10 liters C. 15 liters D. 20 liters E. 30 liters, , 18. Solution A is 20% salt and solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of, , solution B, in what ratio could you mix solution A with solution B to produce 50 ounces of a 50% salt, , solution?, , A. 6:4 B. 6:14 C. 4:4 D. 4:6 E s7, , 19. In a two pound box of nuts and bolts that costs $2.34, the nuts cost 96 cents per pound when purchased, , separately and the weight in the box due to both is equal to the weight due to nuts. How much will two, , pound of bolts cost separately?, , A. $2.76 B. $1.92 C. $1.59 D. $1.41 E. $1.38