CAT Algebra

Reading Test 1

Question No : 1

Q.1 Anil mixes cocoa with sugar in the ratio 3:2 to prepare mixture A, and coffee with sugar in the ratio 7:3 to prepare mixture B. He combines mixtures A and B in the ratio 2:3 to make a new mixture C. If he mixes C with an equal amoutn of milk to make a drink, then the percentage of sugar in this drink will be

Question No : 2

Q.2 There are three persons A,B and C in a room. If a person D joins the room, the average weight of the person in the room reduces by x kg. Instead of D, if person E joins the room, the average weight of the persons in the room increases by 2x kg. If the weight of E is 12 kg more than that of D, then the value of x is

Question No : 3

Q.3 The number of coins collected per week by two coin-collectors A and B are in the ratio 3:4. If the If the total number of coins collected by A in 5 weeks is a multiple of 7, and the total number of coins collected by B in 3 weeks is a multiple of 24, then the minimum possible number of coins collected by A in one week is

Question No : 4

Q4. Ramu is a crooked milkman who mixes water in the milk. He keeps two cans of the mixture with him, one for his premium customers which contains 85% milk and the other for the regular customers which has 70% milk
It is known that the ratio of the number of premium customers and regular customers is 17: 12. If he sells the milk 10% above the cost price to premium customers and 5% above the cost price to regular customers, then find his overall profit percentage (Each customer buys equal quantity of milk and assume the water to be free)

SubQuestion No : 5

Q.5 A farmer mixes 25 ml of water for every 75 ml of pure milk and sells it to a tea-seller. The tea seller sells tea containing milk which has 50% water and the rest pure milk. What percentage of the mixture the tea seller receives from the farmer is replaced with water?

SubQuestion No : 6

Q.6 30 liters of mixture from a tank containing milk and water in the ratio 8:7 is removed and replaced by 30 liters of water. Again 30 liters of the mixture thus formed is removed and 30 liters of water is added. This process is repeated once again, what is the volume of the milk in the solution thus formed, if it is known that the initial volume of the mixture in the tank is 120 liters?

SubQuestion No : 7

Q.7 A vessel A contains diesel and kerosene in the ratio 2:3. Another vessel B contains diesel and kerosene in the ratio of 4:7. Both A and B are filled to the brim. Both the vessels are emptied into a third vessel C. What is the ratio of kerosene and diesel in vessel C?

SubQuestion No : 8

Q.8 Two varieties of rice R1 and R2 cost Rs. 20 and Rs. 50 per kg. In what ratio must R1 and R2 be mixed such that the cost price of the resultant rice is Rs. 45 per kg?

SubQuestion No : 9

Q.9 3 identical containers are completely filled with water-milk mixtures with water and milk in the ratio 2 : 3, 3 : 4 and 4 : 5 respectively. All these mixtures are poured into a bigger container. What fraction of the mixture in the bigger container should be replaced by water so that the resulting mixture has equal quantities of water and milk?

SubQuestion No : 10

Q.10 There are two alloys, A and B, which are made up of iron and copper. A contains iron and copper in the ratio 3:5 while B contains copper and iron in the ratio of 3:7. In what ratio should the alloys be mixed so that the resultant alloy has 50% iron? (All ratios to be taken by weight)

SubQuestion No : 11

Q.11 Lokesh bought Grapes, Milk and Sugar in the ratio of 8:5:3. Further, he knows that grapes are 60% water and milk is 80% water. He put everything together and cooked the mixture for 2 hours during which 25% of the water in the dish got evaporated. What is the ratio of dry grapes to water in the cooked dish? (All ratios and percentages are to be taken by weight)

SubQuestion No : 12

Q.12 A mixture P is formed by removing a certain amount of coffee from a coffee jar and replacing the same amount with cocoa powder. The same amount is again removed from mixture P and replaced with same amount of cocoa powder to form a new mixture Q. If the ratio of coffee and cocoa in the mixture Q is 16:9, then the ratio of cocoa in mixture P to that in mixture Q is

SubQuestion No : 13

Q.13 In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturng employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the averag salary obtained by the manufacturing employees to the average salary obtained by the nonmanufacturing employes is

SubQuestion No : 14

Q.14 A container has 40 liters of milk. Then, 4 liters are removed from the container and replaced with 4 liters of water. This process of replacing 4 liters of the liquid in the container with an equal volume of water is continued repeatedly. The smallest number of times of doing this process, after which the volume of milk in the container becomes less than that of water, is

SubQuestion No : 15

Q.15 A glass contains 500 cc of milk and a cup contains 500 cc of wat. From the glass, 150 cc of milk is transferred to the cup and mixed thoroughly. Next, 150 cc of this mixture is transferred from the cup to the glass. Now, the amount of water in the glass and the amount of milk in the cup are in the ratio

SubQuestion No : 16

Q.16 A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1:3, then the ratio of lemon juice and sugar in the new mixture is