### AVERAGE

Model Questions

1. The average of 5 consecutive odd numbers if the smallest of those numbers is denoted by a is......
A) a + 8     B) a + 7      C) a + 4      D) 7a          E) a + 9
Sol: From the given data, the first odd number is a.
a, a + 2, a + 4, a + 6, a + 8
If numbers are having common differences, the middle number will be average.
So, a + 4 should be the answer.           Ans: C

2. The average weight of a class of 15 students is 40 kgs. When a new student whose weight is 50 kgs replaces an old student, the average weight of the whole class decreases by 1 kg. The weight of the replaced student is....
A) 55 kgs    B) 50 kgs     C) 65 kgs      D) 62 kgs      E) 69 kgs
Sol: Decreased weight = 15(1) = 15kg
So, The weight of the replaced student is
= New student weight + 15
= 50kgs + 15 = 65kgs.            Ans: C

3. There are thrice the number of two wheelers as there are three wheelers and the number of four wheelers are equal to the number of
two wheelers. The average number of wheels per vehicle is....
A) 2     B) 3      C) 4      D) 5      E) 9 4. The average age of 20 men increases by 2 years when one of them, whose age is 60 years, is replaced by a woman. What is the
age of the woman?
A) 68 years    B) 82 years    C) 72 years     D) 100 years     E) 110 years
Sol: Total age increased = 20(2) = 40 years
Age of the woman = 60 + 40 = 100 years              Ans: D

5. The average weight of all the 11 players of the Indian Cricket Team is 60 kg. If the average of first six lightest players is 52 kg and that of the six heaviest players is 63 kg, then the average weight of the player who lies in the sixth position when all the 11 players are arranged in the order of increasing or decreasing weight is:
A) 51 kg     B) 52 kg     C) 30 kg    D) 59 kg      E) none of these 6. The average weight of 10 person's increases by 3 kg when a new person comes in place of one of them weighing 75 kg. What might be the weight of the new person?
A) 105      B) 100      C) 60    D) 50     E) 80
Sol: Weight Increased = 10(3kgs) = 30kgs
New person Weight = 75kgs + 30kgs
= 105kgs                                                     Ans: A

7. The average for first 60 natural numbers is...
A) 22.25     B) 24.25       C) 25     D) 30.5       E) 32.5 8. The average price of three items of furniture is Rs.10000. If their prices are in the ratio 2 : 3 : 5, then the price of cheapest item is...
A) Rs.6000     B) Rs.5000      C) Rs.8000     D) Rs.10000     E) 7000
Sol: Average price = Rs.10000
So, total price of three items = Rs.30000
2x + 3x + 5x = 30000
10x = 30000
x = 3000
So, the price of cheapest item 2x = Rs. 6000                Ans: A

9. The average age of 20 students is 10 years. If the age of their teacher is included, it becomes 11 years. The age of teacher (in years) is...
A) 27 years      B) 31 years      C) 35 years     D) 30 years      E) 32 years
Sol: Age Increased = 21(1) = 21 years Age of teacher

= Initial Average + Age Increased
Age of teacher = 21(1) + 10 = 31 years.     Ans: B

10. The average of all odd numbers upto 150 is
A) 51      B) 75      C) 49.5      D) 49          E) 70 11. The average of 20 numbers is calculated as  30. It is discovered later on that while calculating the average one number, namely 46, was wrongly read as 36. The correct average is :
A) 20      B) 18        C) 30.5       D) 14        E) 25.5 12. The mean of 25 observations was 18. It was found later that an observation 48 was wrongly taken as 13. The correct (new) mean is :
A) 35.2    B) 36.1     C) 19.4     D) 39.1     E) 20.1 13. The average age of eleven cricket players is 25 years. If the age of the coach is also included, the average age increased by
20%. The age of the coach is :
A) 48 years      B) 85 years     C) 40 years     D) 36 years      E) 75 years
Sol: 20%(25 years ) = 5 years increased
Total Age increased = 12(5) = 60 years
So, Age of coach = 60 + 25 = 85 years             Ans: B

14. The average of 7 consecutive odd positive integers is 11. The least one among them is
A) 5     B) 3     C) 1     D) 7     E) 6
Sol: For Consecutive numbers, the middle number is average.
So, 4th number = 11
Then 1st number = 11 − 6 = 5              Ans: A

15. Rahul bought 7 socks at Rs.30 each, 20 shirts at Rs.100 each and 30 belts at Rs.70 each. Find the average price(approximately)
of all the articles.
A) Rs.75.61        B) Rs.45           C) Rs.60       D) Rs.50      E) Rs.70 16. What is the ratio of the average of first 5 prime numbers to the average of first eleven even natural numbers?
A) 1 : 7    B) 7 : 20     C) 9 : 16      D) 7 : 15      E) 5 : 13
Sol: Average of n even numbers = n + 1
= 11 + 1 = 12 17. What is the product of the average of first fifteen positive odd numbers and the average of first twenty positive even numbers?
A) 285.25     B) 144     C) 315    D) 175     E) 350
Sol: Average of first 15 odd numbers = 15
Average of first 20 even numbers = 20 + 1
= 21
So, product = 15 × 21 = 315            Ans: C

18. In a class of 100 students 70% are girls and the remaining are boys. Average marks of boys are 50 and that of girls are 60. What
are the average marks of the whole class?
A) 58    B) 65     C) 66      D) 57       E) 60
Sol: Percentage of boys = 100% − 70% (girls)
= 30%
So, Girls : Boys = 7 : 3 19. In a class the ratio of rural to urban students is 5 : 8. In an examination the average percentage marks of the rural and the urban
students are respectively 78 and 65. What is the overall average percentage marks of the class (correct to two decimal places)? 20. The average of 10 observations was found to be 40. Later on, it was detected that an observation 80 was misread as 20. The correct average of the observations is :
A) 28    B) 46     C) 32     D) 45     E) 36 21. The monthly salary of 50 employees of a factory is Rs.25,300. If three officers are getting Rs.60,000 each and the average salary of 6 supervisors is Rs.60,000, then what is the average salary (in Rs.) of the remaining employees?
A) 17180    B) 17680      C) 17080     D) 17683      E) 17585
Sol: Total Salary of 50 employees = 50 × 25300
Let average salary of the remaining employees = x
So,
50 × 25300 = 3 × 60000 + 6 × 60000 + 41(x) 22. The Average of 9 consecutive numbers is 50. The largest of these numbers is :
A) 24      B) 54      C) 22      D) 20      E) 74
Sol: For consecutive numbers middle number = Average
So, 5th number = 50
Then 9th number = 50 + 4 = 54            Ans: B

23. If the average of five consecutive even numbers be 90, then the greatest number among them is
A) 94      B) 96       C) 92        D) 98               E) 74
Sol: Average = 90
So third number = average = 90
Largest number = 90 + 4 = 94              Ans: A

24. A student, by mistake, wrote 45 in place of 55 as a number at the time of finding the average of 20 given numbers and got the
average as 40. The correct average of these numbers is :
A) 40.5         B) 48.5           C) 42.5           D) 49            E) 50 Examples

1. A batsman has a certain average runs for 16 innings. In the 17th inning he made a score of 85 runs thereby his average is increased by 3. What is his average after 17th inning?Examples

Sol: The average for 17th inning has been increased by 3.
The total increase in the runs for 17th inning = 17 × 3
= 51
But the batsman scores 85.
Average runs in his 16th innings = 85 – 51
= 34.
Hence the average of runs after 17th innings = 34  + 3
= 37

2.  A man has 7 children. When their average age was 12 years, the child who was 6 years of age, died. What was the average age of surviving children 5 years after the death of the above child?
Sol: Average age of 7 children  = 12 years
Total age of 6 children  =  12 × 7 = 84 years
Total age of 6 children after the death of a child aged 6 years = 84 – 6 = 78
Hence   the average age of the surviving children = After 5 yrs. = 13 + 5 = 18 yrs.

3.  If the weights of 5 students of a class are 49.6 kg, 39.8 kg, 45.2 kg and 24.6 kg respectively then what is their average weight?
Sol: Total weight of 5 students = 49.6 + 39.8 + 40.8 + 45.2 + 24.6
= 200 kg.
∴    Their average weight = = 40 kg.

4.  The average temperature for Monday, Tuesday and Wednesday was 36oC. The average temperature for Tuesday, Wednesday and Thursday was. If the temperature for Thursday was 37oC, what was the temperature on Monday?
Sol: Average temperature for Monday, Tuesday and Wednesday = 36oC
Total temperature for Monday, Tuesday and Wednesday = 36 × 3
= 108oC
∴   Average temperature for Tuesday, Wednesday and Thursday = 38oC
∴    Total temperature for Tuesday, Wednesday and Thursday = 38 × 3
= 114oC
∴    Total temperature for Tuesday and Wednesday only = 114 – 37
=  77oC
∴    Temperature for  Monday only = 108 – 77
= 31oC

5.  A train covers the first 16 km at a speed of 20 km per hour another 20 km at 40 km per hour and the last 10 km at 15 km per hour. Find the average speed for the entire journey. 6.  A vehicle travels from A to B at the speed of 40 km/hr, but from B to A at the speed of 60km/hr. what is its average speed during the whole journey?
Sol: Let the distance from A to B be x km 7.  The average age of a class of 40 boys is 16.95 years. A new boy joins the class and the average age now is 17 years. What is the age of the new boy?
Sol: The average age of 40 boys  = 16.95 years Total are of 40 boys  = 16.95 × 40
= 678 years
The average age of 41 boys  = 17 years Total age of 41 boys  = 17 × 41
= 697 years Age of the new boy  = 697 – 678
= 19 years

The average of the given quantities is calculated by dividing the sum of the quantities by their number. If the average of ‘x’ quantities is ‘a’ and average of ‘y’ quantities is ‘b’, then average of x and y is

Weighted Average
Let x1, x2, x3, …..xn be the quantities and w1, w2, w3, ….wn be the weights attached to them then Weighted Average

SOLVED EXAMPLES

Example 1. A cricketer has completed 18 innings and his average is 26.5 runs. How many runs must he make in his next innings so as to raise his average to 27?
(1) 36           (2)46            (3)38            (4) 40            (5) None of these
Explanation:
(1)   Formula = n(y – x) + y
n = 18
x = 265
y = 27
= 18(27 – 26.5) + 27
= 9 + 7
= 36

Example 2. The average of 13 numbers is 30. The average of 1st 7 of these numbers is 32 and the last 7 of these numbers is 22. Find the 7th number.
(1) 15         (2) 16          (3) 12          (4) 20          (5) None of these
Explanation:
(3)    Total number = 13 × 30 = 390
1st 7 numbers = 7 × 32 = 224
Last 7 number = 7 × 22 = 154
7th number = 390 – (224 + 154)
= 12

Example 3. The average of marks obtained by 65 candidates in a certain examination is 25. If the average marks of passed candidates is 27 and that of the failed candidates is 14, what is the no. of candidates who passed the examination?
(1) 53            (2) 64            (3) 55            (4) 70            (5) None of these
Explanation:
(3)  Passed candidates = x
Failed candidates = 65 – x
Total marks ∴   25  ×  65 = 27x + (65 – x)14
⇒ 1625 = 27x + 910 – 14x
⇒ 13x = 715
⇒ x = 55

Example 4. In a class there are 30 students whose average is decreased by6 months, when 4 students aged 16, 17, 18 and 19 years respectively are replaced by the some no. of students. Find the average of the new students.
(1) 16.25               (2) 15.25               (3) 16               (4) 15.75               (5) None of these Example 5. The average age of 11 persons in a committee is increased by 2 years when three men aged 32 years, 33 years and 34 years are substituted by three women. Find the average age of these three women.
(1) 40 1/3        (2) 40          (3) 41 1/3        (4) 41 years          (5) None of these Example 6. The average of 40 numbers is 405. If each of the numbers is divided by 15. Find the average of new set of numbers.
(1) 27          (2) 28          (3) 21          (4) 26          (5) None of these

Explanation:

405/15 = 27

Example 7. The average age of 80 boys in a class is 15. The average age of a group of 15 boys in the class is 16 and the average age of another 25 boys in the class is 14. What is the average age of remaining boys in the class. (approx.)
(1) 20          (2) 15          (3) 18          (4) 21          (5) None of these
Explanation:
(2)    Remaining boys average age = x
⇒ 15 × 16 + 25 × 14 + 40x = 80 × 15
⇒ 240 + 350 + 40x = 1200
⇒ 40x = 1200 – 590
x = 610/40
x = 15. 25

Example 8. A batsman in his 12th innings makes a score of 63 runs and there by increases his average score by ‘2’. The average of his score after 12th innings is.
(1) 39        (2) 41         (3) 37         (4) 45         (5) None of these
Explanation:
(2)    Average score = x till 11 innings
Total runs = 11x
Total runs after 12th inning = 11x + 63
Average after 12th inning = ( x + 2)
Total run = 12 ( x + 2)
12 ( x + 2) = 11x + 63 ⇒ x = 63 – 12 × 2 = 39
Average of his score = 39 + 2 = 41

Example 9. A certain amount was to be distributed among the A, B and C in the ratio 2 : 3 : 4 but was erroneously distributed in the ratio 7 : 2 : 5 as a result of this ‘B’ received Rs. 40 less. What is the actual?
(1) 210         (2) 270         (3) 230         (4) 280         (5) None of these Example 10. Two number are respectively 20% and 50% more than a third number. The ratio of the two numbers is.
(1) 2 : 5         (2) 4 : 5        (3) 3 : 5        (4) 6 : 7        (5) None of these PRACTICE EXERCISE

1. The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that  of the failed candidates is 15. What is the number of candidates who passed the examination?
(1) 90        (2) 85         (3) 100         (4) 120         (5) None of these
Ans: 100

2. The average salary of all workers in workshop is 8000. The average salary of 7-technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the work shop is.
(1) 20         (2) 21         (3) 23         (4) 22         (5) None of these
Ans: 21

3. In a competitive examination, the average marks obtained was 45. It was later discovered that there was some error in computerization and the marks of 90 candidates had to be changed from 80 to 50, and the average come down to 40 marks. The total number of candidates appeared in the examination.
(1) 500         (2) 600         (3) 540         (4) 580         (5) None of these
Ans: 540

4. The average weight of A, B, C is 84 kg. If D joins the group the average weight of the group becomes 80 kg. If another man ‘E’ who weights is 3kg more than D replace A, then average of B, C, D and E becomes ‘79’ kg. What is the weight of ‘A’
(1) 64        (2) 72         (3) 75         (4) 100         (5) None of these
Ans: 75

5. 1/3rd of certain journey is covered at the rate of 25kmph. 1/4th at the rate of 30 kmph and the respect 50 kmph. Find the average speed for the hole journey .
(1) 33.33 kmph         (2) 36 kmph         (3) 42 kmph         (4) 27 kmph         (5) None of these
Ans: 33.33 kmph

6. Deepak’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Deepak and he thinks that Deepak’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Deepak.
(1) 67 kg         (2) 68kg         (3) 69 kg         (4) 70 kg         (5) None of these
Ans: 67 kg

7. The average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of the failed candidates is 15. What is the number of candidates who passed the examination?
(1) 90         (2) 85          (3) 100          (4) 120          (5) None of these
Ans: 100

8. The average age of Raju & Aditya is 35 years. If Raghu replaces Raju. The average age becomes 32 years and if Raghu replaces Adithya then the average becomes 32 years. If the average age of Naveen and Ramu behalf of the average age of Raju, Aditya and Raghu. Then the average age of all the people-?
(1) 28          (2) 32          (3) 35          (4) 30          (5) None of these
Ans: 28

9. The average salary is being paid to all it’s employees by a company is 15,500. The average salary of the senior employees is 18000 per month and the average salary of the junior employees is 12000 per month. If there are only two levels of employees viz junior and senior levels, then what fraction of the total employees is the too junior level employees are
(1) 7/5    (2) 7/12       (3) 5/12       (4) 5/7         (5) None of these
Ans: 7/12

10. The average age of ‘8’ persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. Find the average age of these two women.
(1) 48           (2) 36          (3) 42          (4) 29          (5) None of these
Ans:  48

The average of the given quantities is calculated by dividing the sum of the quantities by their number.
Average = Sum of the quantities / Number of quantities

Weighted average: Let x1, x2, x3, ...... xn be the
quantities and w1, w2, w3, ...... wn be the weights attached to them
then Weighted Average = w1x1 + w2x2 + w3x3 + ........ + wnxn / w1 + w2 + w3 + ........ + wn

MODEL QUESTIONS
1. The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number?
A) 9           B) 27           C) 32           D) 35

2. The average of 17 results is 60. If the average of first 9 results is 57 and that of the last 9 results is 65. What is the value of 9th result? (SSC-CGL – 2017)
A) 39         B) 78         C) 117         D) 156

3. In a class, the average age of 23 boys is 12 years and the average age of 17 girls is 11 years. What is the average age of the whole class?
A) 11.5 years      B) 11.245 years     C) 11.575 years      D) 11.525 years

4. In a class, the average score of thirty students on a test is 69. Later it was found that the score of one of the students was wrongly read as 88 instead of 58. The actual average score is (SSC-CGL – 2019)
A) 71           B) 78           C) 65           D) 68

5. The average of 23 numbers is 28. Later, it was pointed out that value of one the numbers was wrongly taken as 78 instead of 87. What is the correct average?
A) 31.25     B) 27.15     C) 28.39     D) 32.65

6. Out of 6 numbers the sum of the first 5 numbers is 7 times the 6th number. If their average is 136, then the 6th number is.... (SSC-CGL – 2019)
A) 102         B) 96         C) 84         D) 116

7. A cricketer’s average for 11 matches is 25 runs. In the next four matches he scored 72, 34, 51 and 48 runs. Find his new average for the 15 matches?
A) 39          B) 32          C) 36          D) 28

8. The average age of a class of 24 students is 11 years. If the teacher’s age is also included, the average increases by one year. Find the age of the teacher?
A) 35           B) 39           C) 34           D) 36

9. The average age of six members of a family is 20 years. If the age of the servant is included, then the average age increase by 25%. What is the age of the servant (in years)? (SSC-CGL – 2017)
A) 30           B) 55           C) 50           D) 35

10. The average weight of 8 persons increases by 1.5 kg when a person weighting 65 kg is replaced by a new person. What could be the weight of the new person?
A) 55 kg     B) 57.5 kg     C) 75 kg    D) 77 kg

11. The average of twelve numbers is 45.5. The average of the first four numbers is 41.5 and that of the next five numbers is 48. The 10th number is 4 more than the 11th number and 9 more than the 12th number. What is the average of the 10th and 12th number? (SSC-CGL – 2019)
A) 46.5         B) 46         C) 47.8         D) 47

12. 5 kg sugar is purchased at Rs.10 per kg, 6kg at Rs.11 and 9kg at Rs.12 per kg. What is the weighted average price of sugar per kg?
A) 8.8        B) 10.8        C) 11.2        D) 11.8

13. The average of 12 numbers is 9. If each number is multiplied by 2 and added to 3, the average of the new set of numbers is (SSC-CGL – 2016)
A) 9           B) 18           C) 21           D) 27

14. In a class, average height of all students is 'a' cms. Among them, average height of 10 students is 'b' cms and the average height of the remaining students is 'c' cms. Find the number of students in the class. (Here a > c and b > c) (SSC-CGL – 2016) 15. The average weight of some students in a class is 68.5 kg. If four new students of 72.2 kg, 70.8 kg, 70.3kg and 66.7 kg are enrolled in the class, the average weight of students increases to 300 g. Initially how many students were there in the class? (SSC-CGL – 2018)
A) 11          B) 26          C) 21          D) 16

ANSWERS: 1-B; 2-B; 3-C; 4-D; 5-C; 6-A; 7-B; 8-D; 9-B; 10-D; 11-A; 12-C; 13-C; 14-D; 15-D.

Explanations
1.
The total of seven numbers = 7 × 18 = 126
The total of first 3 and last 3 numbers is = 3 × 14 + 3 × 19 = 99
∴ Middle number is (126 − 99) = 27

Shortcut: 3 × (−4) + 3 × (+1) = −12 + 3 = −9
∴ Middle number = 18 + 9 = 27

2. The total of 17 numbers = 17 × 60 = 1020
The total of first 9 and last 9 numbers is = 9 × 57 + 9 × 65 = 1098
∴ Middle number is (1098 − 1020) = 78

Shortcut:  9 × (−3) + 9 × (+5) = −27 + 45 = +18
∴ Middle number = 60 + 18 = 78

3. Total age of 40 students = (23 × 12 + 17 × 11) = 463
Average age = 463/40 = 11.575 years

Shortcut: Let all the students average be 11 years
Extra age by all boys = 23 × 1 yr. = 23 years
Extra average for all 40 students = 23/40 = 0.575
∴ Actual Average = 11 + 0.575 = 11.575

4. The Correct Average Shortcut:
Additional score taken = 88 − 58 = 30
Additional average = 30/30 = 1
∴ New average is 69 − 1 = 68

5. Correct Average Shortcut: Value less taken = 87 − 78 = 9
Average less taken = 9/23 = 0.39
∴ New average is 28 + 0.39 = 28.39

6. Let the 6th number be ‘X’ ∴ 7x = (136 × 6) − x
⇒ x = 102

7. Total runs in 11 matches = 11 × 25 = 275 runs
Total runs in the next 4 matches
= 72 + 34 + 51 + 48 = 205 runs = 32 runs

Shortcut: Let the average of all 15 matches be 25 Extra runs in 4 matches
= (72 − 25) + (34 − 25) + (51 − 25) + (48 − 25) = 105
Extra Average = 105 /15 = 7
∴ New Average = 25 + 7 = 32

8. Total of 24 students is 24 × 11 = 264 years
Total age with teacher is 25 × 12 = 300 years
∴ Teacher’s age is 300 − 264 = 36 years

Shortcut: Teacher’s age = 11 + (25 × 1) = 36 years

9. Total age of the family is 6 × 20 = 120 years
Average age after servant’s inclusion
= 125% of 20 = 25 years
Total age with servant = 7 × 25 = 175 years
∴ Servant’s age is 175 − 120 = 55 years

Shortcut: Servant’s age = 20 + (7 × 5) = 55 years

10. Let the average weight of 8 persons be ‘x’ years and the age of the new person be ‘y’ years Shortcut: 65 + 8 × 1.5 = 77 kg

11. The total of 12 numbers = 12 × 45.5 = 546
The total of first 4 and next 5 numbers is
= 4 × 41.5 + 5 × 48 = 406
Total of 9th, 10th & 11th numbers = 546 − 406 = 140
Let the 10th number be x
∴ x + x − 4 + x − 9 = 140
⇒ x = 51 Shortcut: 4 × (− 4) + 5 × (+ 2.5) = − 16 + 12.5 = − 3.5
∴ Total of 9th, 10th & 11th numbers
= (45.5 × 3) + 3.5 = 140
Let the 10th number be x
∴ x + x − 4 + x − 9 = 140
⇒ x = 51 = 46.5

12. Weighted average Shortcut: Let the assumed average be Rs. 10 13. New average Shortcut: New average = (9 × 2) + 3 = 21

14. Let the number of students be ‘x’ 15. Let the number of students be ‘x’ ⇒ 68.5x + 280 = 68.8(x + 4)
⇒ 68.5x + 280 = 68.8x + 275.2
⇒ 0.3x = 4.8 Posted Date : 29-08-2022

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.