Average Mixture & Alligation Level-3 Quiz-3

1. Find the average of all the three-digit numbers whose units digits are three times their hundreds digits.

2. An educational institution runs six branches. The number of students in each of the branches and the average score of the students in each branch in a certain test are given below. What is the approximate weighted average score of the students of the institution? branch no. – no. of students – avg. marks (1-225-60), (2, 205, 56), (3, 180, 55), (4, 195, 70), (5, 220, 65), (6, 250, 80)

3. Consider the set S = {2, 5, 8, … 89}; subsets A, B, C, D and E of S are defined as the sets containing all the numbers of the forms 5k, 5k + 1, 5k + 2, 5k + 3 and 5k + 4, respectively, where k is a whole number. The averages of all the numbers in A, B, C, D and E are a, b, c, d and e, respectively. Which of the following is true?

4. A vessel contains an 80% alcohol solution. 20% of the solution was removed and replaced with water. If this process is repeated, find the percentage of alcohol which remains in the solution.

5. A local grocer mixed three qualities of coffee T 1 , T 2 and T 3 priced at Rupees 79 per kg, Rupees 64 per kg and Rupees 62 per kg, respectively in the ratio 1 : 2 : 4. To 4 kg of this mixture he adds quantities of T 1 and T 3 which are in the ratio 1 : 5. He now sells this new mixture for Rupees 77.88 per kg thereby making a profit of 20%. How much of T 1 did he mix with the mixture?

6. Vessels A and B contain mixtures of milk and water. A has a% milk and B has b% milk. Mixture P is formed by mixing a% of vessel A’s contents with (100 – b)% of vessel B’s contents. Mixture Q is formed by mixing (100 – a)% of vessel A’s contents with b% of vessel B’s contents. Mixtures P and Q have k% milk each. If a ≠ b, find a + b.

7. A vessel is filled to its capacity with pure milk. Nine liters are withdrawn from the vessel and replaced with an equal amount of water. Nine liters of the mixture is again withdrawn and then replaced with an equal amount of water. After these changes, the vessel contains 17.1 liters
of milk less than it did initially. Find the capacity of the vessel. (in liters).

8. There are five solutions A, B, C, D, and E with concentrations 10%, 20%, 40%, 50%, 80%, respectively. (X, Y) denotes a mixture of X and Y in which X and Y are mixed in some proportion, such that both are included. Similarly (X, Y, Z) denotes a mixture in which X, Y and Z are mixed in some proportion, such that each is included. Which of the following cannot have a concentration of 75 %?

9. Two large drums A and W, have 1000 liters of alcohol and 1000 liters of water, respectively. Two liters of the contents in drum A are removed and mixed with the contents of drum W. This is the first operation. Two liters of the contents of drum W are then mixed with the contents of drum A. This is the second operation. The first and the second operations together constitute process P. Process P is carried out 3 times. After that, only the first operation is done. After this, ‘a’ is the alcohol in the first drum and ‘w’ is the water in the second drum. What is the relation between a and w?

10. There are two vessels, A and B, of equal capacity. A is filled completely with pure benzene and B is left empty. Each operation involves transferring some quantity of liquid from A to B and then refilling A with the same quantity of water. At the end of n such operations (n > 1), it is ensured that B is full. If n = 2, then what is the maximum possible concentration of water in B?