ROHRA’S ACADEMY Averages and AlligationFind the AM of:-

1) 21, 22 and 262) 45, 34, 11, 26 and 843) 1, 3, 5, 7,…, 194) 1, 2, 3, …, 405) 22, 24, 26,…, 50

Find the GM of :-1) 4 and 92) 12, 9, 163) 1, 2, 4, 84) 16 and 255) 1, 2, 3, 4, 5

Find the median for 1) 31, 54, 11, 12, 89, 901, 100. 2) 12, 78, 54, 1, 3, 9.

Find the mode for 1) 2, 6, 8, 9, 1, 3, 10, 1, 3, 4, 8, 4, 10, 3. 2) 1, 2, 3, 4, 5

LEVEL – 11) Find the average of the first 10 whole numbers.

2) The average of 12 numbers is 32. What will be the average if one more number whose value is 32 is added to the group.

3) The average age of a group of 10 students is 11 and that of another group of 6 students is 19. Find the average of the combined group.

4) The average of 8 numbers is 12. Find the square of their sum.

5) Find the AM, HM and GM of 1, 2 and 4 and arrange them in ascending order.

6) Two years ago, the average age of 5 brothers was 12. Find the present average.

7) The average of 4 numbers is 12 and that of the first three is 11. Find the fourth number.

8) The average of 4 numbers is 12 and that of the first two is 11. Find the fourth number.

9) Of the three numbers, A, B and C, A is twice as much as B and B is triple of C. The average of these three numbers is 20. Find A, B and C.

10) The average of 10 numbers is 10. What will be the new average if each of the first five numbers is increased by 4.

LEVEL – 211) The average weight of a class of 20 students is 49 kgs. If two students with weights 51

and 54 are replaced by two new students with weights 80 and 75 respectively, find the new average of the class.

1. 47 2. 50 3. 51.5 4. Cannot be determined

12) The average age of a class of 20 students is 12. If the teacher joins the group the average increases by 2. Find the age of the teacher.

1. 40 2. 54 3. 24 4. 44

13) While traveling from Bombay to Goa, the speed of a car is 80 kmph and while returning, the speed is 120 kmph. Find the average speed of the car throughout the journey.

1. 100 kmph 2. 110 kmph 3. 90 kmph 4. 96 kmph

14) In what ratio should coffee at Rs.120 per kg be mixed with coffee at Rs.190 per kg to get a mixture priced at Rs.145 per kg.

1. 7 : 4 2. 9 : 5 3. 5 : 9 4. Cannot be determined

15) The average salary of 15 officers is Rs.12000 and the average salary of non-officers is Rs.4000. Find the total number of employees if the average salary of the firm is Rs.7000.

1. 40 2. 25 3. 30 4. 50

LEVEL – 321) Total expenses of a boarding house are partly fixed and partly varying linearly with tile number of boarders. The average expense per boarder is Rs. 700 when there are 25 boarders and Rs. 600 when there are 50 boarders. What is the average expense per boarder when there are 100 boarders?1. 550 2. 560 3. 540 4. 560

22) A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got morethan 50% marks is:1. 2 2. 3 3. 4 4. 5

23) Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?1. 1050 2. 540 3. 1440 4. 1590

24) Three math classes: X, Y, and Z, take an algebra test.The average score in class X is 83.The average score in class Y is 76.The average score in class Z is 85.The average score of all students in classes X and Y together is 79.The average score of all students in classes Y and Z together is 81.What is the average for all the three classes?1. 81 2. 81.5 3. 82 4. 84.5

25) Amol was asked to calculate the arithmetic mean of ten positive integers each of which had two digits. By mistake, he interchanged the two digits, say a and b, in one of these ten integers.

As a result, his answer for the arithmetic mean was 1.8 more than what it should have been. Then b – a equals1. 1 2. 2 3. 3 4. none of these

26) Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 years and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to1. 23 2. 22 3. 21 4. 25 5. 24

27) An alloy of iron and nickel is taken in the ratio of 1:2 and another alloy of the same metals is taken in the ratio of 2:3. How many parts of the two alloys must be taken to obtain a new alloy consisting of iron and nickel in the ratio 3:5?1. 3 and 5 2. 2 and 9 3. 2 and 5 4. 1 and 5 5. 3 and 5

28) If the ratio of harmonic means of two numbers to their geometric means is 12 : 13, find the ratio of the numbers.1. 4 :9 2. 8 : 9 3. 4: 5 4. 9:4 5. Options 1 or 4.

Directions for questions 29 and 30 - The batting average (BA) of a test batsman is computed from runsscored and innings played—completed innings and incomplete innings(not out) in the following manner:r1 = number of runs scored in completed inningsn1 = number of completed inningsr2 = number of runs scored in incomplete inningsn2 = number of incomplete innings.

BA = (r1 + r2)/n1

To better assess a batsman’s accomplishments, the ICC is consideringtwo other measures MBA1 and MBA2 defined as follows:MBA1 = (r1/n1) + (n1/n2) + max[0, (r2/n2) – (r1/n1)]

MBA2 = (r1+ r2)/(n1 + n2)

29. Based on the information provided which of the following is true?1. MBA1≤ BA ≤ MBA2

2. BA ≤ MBA2 ≤ MBA1

3. MBA2 ≤ BA ≤ MBA2

4. None of these

30. An experienced cricketer with no incomplete innings has a BA of50. The next time he bats, the innings is incomplete and he scores 45 runs.It can be inferred that:1. BA and MBA1 will both increase2. BA will increase and MBA2 will decrease3. BA will increase and not enough data is available to assesschange in MBA1 and MBA2

4. None of these