Average

In general average is the central of the data provided. If A has an amount of 300 INR ,B has 500 , and C has 800, then average amount off all the tree persons is –\frac{300+400+800}{3}.
i.e 500 INR.
There are some properties and short tricks which must be remember to solve these type of sums in a minute in the competitive exams.
a) The average of any two or more quantities always lies between the lowest and highest values of the data provided.
b) If each number is increased/decreased by X of a given data then the average of the data is also increased/decreased by X.
c) if each number is multiplied/ divided by X of a given data then the average of the data is the product of old average and X or 1/X .
d) The average of the sum of ‘n’ natural numbers is- \frac{n+1}{2}.
e) The average of the square of the sum of ‘n’ natural numbers is- \frac{(n+1)(2n+1)}{6}.
f) The average of the Cube of the sum of ‘n’ natural numbers is- \frac{n(n+1)^2}{4}.
g) The average of the ‘n’ even numbers is – “n+1”
To be continue………………………..
Type-1
1) The Average temperature for Monday, Tuesday, Wednesday and Thursday was 35 degree centigrade. The average temperature of Thursday , Friday, and Saturday was 38 degree centigrade. The average temperature for Monday to Saturday was 36 degree centigrade, find the temperature for Thursday:- a) 35.5, b) 37.5, c) 39, d) none of these.

Total temperature of M+T+W+TH = 35*4
=140
Total temperature of Thur + Fri+ Sat = 38*3
=114
Total temperature for Mon to Sat is 36* 6
=216
Mon to Sat + Thurs = 140+114
= 254
Temperature of Thurs = 254-216
= 38
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2) Average rainfall on Monday, Tuesday, Wednesday, and Thursday is 420.5 cm and the average on Tuesday, Wednesday, Thursday and Friday is 440.5 cm. If the ratio of rainfall for Monday and Friday is 20:21. Find the rainfall in cm on Monday and Friday:- a) 1700,1470, b)1682,1762, c)1800,1890, d)1600,1680.

Mon to Thurs total rainfall = 420.5*4
= 1682 cm.
Total rainfall of Tues to fri = 440.5*4
=1762 cm
The difference in rainfall of friday and monday is = 1762 – 1682
= 80
The difference in the ratio of Friday and Monday = 21-20
= 1
1 equals to 80
so the rainfall of Mon and fri are 1600 & 1680.
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3)The average rainfall in January and February is 6 cm and from March to June is 5 cm and July to October is 10 cm and in November and December, it is 6 cm. The average rainfall for the whole year is:- a) 7, b) 5.5, c) 7.5, d) None of these.

Total rainfall of Jan & Feb is 6*2
=12 cm
Total rainfall of march to june is 5*4
=20 cm
Total rainfall of July to October is 10*4
=40 cm
Total rainfall in Nov & Dec is 6*2
=12 cm
So total rainfall in the whole year is 84 cm
The average rainfall of the year = 7cm
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4) If the mean temperature of Monday to Wednesday was 37 degrees centigrade and Tuesday to Thursday was 34 degrees centigrade. If the temperature on Thursday was 4/5 that of Monday, the temperature on Thursday was:- a) 36.5, b) 36, c) 35.5, d) 34.

The temperature of Monday to Wednesday is 37*3
= 111 degree centigrade.
The Temperature of Tuesday to Thursday is 34*3
= 102 degree centigrade.
Now, Monday – Thursday = 9 degree centigrade.
Thursday was 4/5 of Monday.
Let Monday be X so, Thursday be 4x/5.
Now, x/5 = 9
X= 45 degree centigrade
The temperature of Thursday was 4/5 of 45
= 36 degree centigrade.
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5) The average of the first four of five numbers is 26 and that of the last four is 25. The difference between the last number and the first number is:- a) 1, b)4, c)5, d)16.

The average of the first four number is 26
so total =26*4
=104.
The average of the Last four numbers is 25.
So total = 100
So the difference between the First and last number is (104-100) = 4.
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6) Out of five numbers, the average of the first three is 15 and that of the last three is 16. If the last number is 19, the first is:- a) 16, b) 18, c) 19, d) 15.

The average of first three is 15
so total of first three is 45.
The average of last three is 16.
so total of last three is 48.
Now the difference of the above two gives last- First = 3
Last number is 19, so the first number is 16.
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7) The Average of 11 results is 60 marks. If the average of the first six results is 59 marks that of the last six is 62 marks, then the sixth result contains. a) 60, b) 61, c) 65, d) None of these.

The average of 11 results is 60
Then total = 660
The average of first six results is 59
Then total = 354.
the average of the last six = 62
Then total =382.
SO the Sixth number is (354+382) – 660
= 76.
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8) Out of five numbers the average of the first four numbers is twice the fifth number. If the average of the numbers is 27, then the fifth number is:- a) 45, b) 25, c) 20, d) 15.

Average of the five numbers is 27
so total is 135.
Let Fifth number be X
Then average of first 4 numbers is 2X
Then total of first 4 numbers is 8X
Now, 8X+X = 135
X = 15.
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9)The average of 13 result is 60. If the average of first 7 result is 59 and that of the last 7 results is 61. What will be the 7th result:- a) 90, b) 50, c) 60, d) 75.

The average of the 13 result is 60
So,Total of the 13 result is 780.
The average of the first 7 result is 59
So Total = 413.
The average of the last 7 results is 61
So total = 427
Now, The seventh result be (413+427)-780
= 60.
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10)The average age of the 30 girls is 13 years, The average age of 18 girls is 15 years. Find out the average age of the remaining 12 girls:- a) 12yrs, b) 10Yrs, c)16Yrs, d) 10.5 yrs.

The average age of the 30 girls is 13
So the total age of 13 girls is 390.
The average of the 18 girls is 15
the total age of the 18 girls is 270.
So the total age of the remaining 12 girls = 120
Average of the 12 girls = 10.
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Type-2
1) A Batsman’s average score for a number of innings is 21.5. In the next four innings his score 4,19,12,12 there by his average decrease by 1.5. Find the total number of innings played by him. a) 22, b) 24, c) None of these.
2) A batsman in his 17th innings makes a score of 63 there by increase his average by 2 runs. Find his original average:- a) 29, b) 30, c) 31, d) None of these.
3) A cricketer has an average of 43 runs in 24 innings. How many runs must he score in 25th innings to makes his average 50:- a) 54, b) 64, c) 74, d) 70.
4) The average of runs of a cricket player in 15 matches 33. If the average of the first 10 matches is 45, then the average of the last matches is:- a) 9, b) 13.5, c) 15, d) 23.
5) Sachin Tendulkar has a certain average for 11 innings. In the 12 innings he scores 120 runs and thereby increase his average by 5 runs. his new average is:- a) 60, b)62, c) 65, d) 66.
6) A cricketer played 80 innings and scored an average of 99 runs. His score in the last inning zero run. To have an average of 100 at the end his score in the last innings should have been. a) 60 runs, b) 80, c) 10, d) 1.
7)In a 10 innings game cricketer scores an average of 49 runs in his first 9 innings. He likes into make an average of 50 runs in 10 innings. What scores he makes in the last innings. a) 51 runs, b)55, c)59, d) 60.
8) The average of the test scores of a class of M students is 70 and that of N students is 91. When the scores of both the classes are combines, the average is 80. What is N/m. a) 10/13, b) 10/11, c) 11/10, d) 13/10.
9) A batsman in his 16th innings makes a score of 60 and thereby increase his average by 3. What is his average after the 16th innings. a) 18, b) 20, c) 15, d) 21.
10) A cricketer has a certain average of 1 innings. In the eleventh innings, he scored 216 runs, thereby increase his average by 12 runs. Find out his new average. a) 96, b) 84, c)97, d) 87.
Type-3
1) If the average age of mother and her daughter is 34.5 years. while the age of the daughter is half of that of the mother. What is the mother’s age? a)48yrs, b) 69, c) 56, d) 46.
2) The average age of Ramesh, Pradip, and his brother, 3 yrs ago was 27 yrs and that pradip and his brother, 5 yrs ago was 20 yrs. What is the Ramesh present age. a) 35 yrs, b) 40, c)45, d)30.
3) 3 Yrs ago, he average age of a family of 5 members was 17 yrs. A baby having been born, the average age of the family is the same today. What is the present age of the Baby. a) 3Yrs, b) 5, c) 2, d)4.
4)The average age of father and son is 25 yrs that of father and mother is38 yrs. The mother is older then her son by:- a) 24, b) 26, c) 28 ,d) 29.
5)The ratio between A and B is 3:5 and the sum of their ages is 56 yrs. The ratio between their ages 7 year ago was:- a) 1:2, b) 2:3, c) 3:4, d) 3:5.
6) In a family of 5 members, the average age at present is 33 yrs. The youngest member is 9 yrs old. The average age of the family just before the birth of the youngest member was:- a) 25, b)24, c) 30, d) 29.
7) The average age of 40 students is 15 years. The average age is increases by 0.2 yrs, when 10 new students are included. Find out the average age of new students. a) 15.2, b) 16, c) 16.2, d) 16.4.
8) The average age of 5 Sister is 20 Yrs. If the age of the youngest sister be 4 yrs. What was the average age of the group of sister at the birth of the youngest sister. a) 25, b)15, c) 18, d) 20.
9)The average age of the four members of a family is 25 yrs. If the head of the family is included in this group then average age increases by 20%. Find out the age of the head:- a) 45, b) 50, c) 55, d) 60.
10)The average age of 20 students of a class is 12 years. If their teacher’s age is also included then the average age is increased by 1 year. Find the age of the teacher. a) 25, b) 30, c) 33, d) 35.
Type-4
1) The average of 4 consecutive even numbers is 27. The largest of these numbers is:- a) 32, b)28, c)30, d) 34.
2)If the average of 6 consecutive numbers is 25, the difference between the largest and the smallest number is:- a) 8, b) 10, c) 12, d) 14.
3) The average of 8 consecutive number is 6.5. The average of the smallest and the greatest numbers among them will be:- a) 4, b) 6.5, c) 7.5, d)9
4) Of the three numbers, the first number is twice of the second and the second is thrice of the third number. If the average of these 3 numbers is 20, then the sum of the largest and the smallest number is:– a) 24, b) 42, c) 54, d) 60.
5) The average of four numbers is 60. First number is 1/4 of the sum of the last three numbers then find the first number:- a) 15, b) 45, c) 42, d) 48.
6) The average of the five consecutive number is 42. Then find the difference between the larger and the smaller number:- a) 4, b) 6, c) 8, d) 12.
7) The sum of the three consecutive odd numbers is 20 more then the first number. Then find the middle number. a) 7, b) 9, c) 11, d) 13.
8) The first number is twice the second and second is twice the third number. If the average of the three number is 21. Then find the smallest number:- a) 9, b) 6, c) 12, d) 18.
9) The average of the 6 consecutive number is 48 then find the difference between the larger and the smaller number:- a) 10, b) 12, c) 9, d) 18.
10) Average of the two numbers is 7.5 and square root of their product is 6. What are the numbers: a) 13 & 2, b) 9 & 6, c) 10 & 5, d) 13 & 3.
Type-5
1) The average of marks of 40 students in an English exam is 72. Later it is found that three marks 64, 62 and 84 were wrongly entered as 68, 65 and 73. The average after mistakes rectified is:- a) 70, b) 72, c) 71.9, d) 72.1.
2) The average age of a group of 30 boys is 12 years. When 2 new boys join them the average increase by 1/4 year. What is the average age of the two new boys:- a) 12, b) 13, c) 14., d) 16.
3)Average age of 38 students is 14 years. If the age of the teacher is included, the average becomes 14 yeas and 4 months. Then teacher’s age is:- a) 23, b) 27, c) 25, d) 29.
4) While calculating average of 5 numbers a students wrote one number as 54 instead of 45 by mistake. As a result, he got the average as 52. The correct average of the numbers is:- a) 50.4, b) 50.2, c) 50.1, d) 50.0.
5) In a cricket team the average age of 11 players is increased by 2 months when 2 players whose age’s are 18 and 20 years are replaced by 2 new players find the average age of the new players. a) 19 yrs 1 months, b) 19 yrs 6 months, c) 19 yrs 11 months, d) 19 years 5 months.
Type-6
1) The average salary of all the staff in an office of a corporate house is Rs 5400. The average salary of the officers is Rs 14000 and that of the rest is Rs4000. If the total numbers of staff is 500, the number of officers is:- a) 10, b) 15, c) 70, d) 50.
2) The average salary of workers in a factory is Rs 6000. There are 12 officers having an average wage of Rs 14000, While average wage of the remaining persons is Rs 5600, the number of the workers is that factory is:- a) 240, b) 230, c) 242, d)252.
3) The average salary per head of all the workers of an institution is Rs 60. The average salary per head of 12 officers is Rs 400. The average salary per head of the rest is Rs 56. Then the total number of workers in the institution is:- a) 1062, b) 1060, c) 1030, d) 1032.
4) A man spend an average of Rs 1,694.70 per month for the last 7 months and Rs 1,810.50 per month for the next 5 months. His monthly salary if he saves Rs 3084.60 during the whole year is:- a) 1000, b) 2000, c) 2400, d) 3000.
5) The average income of employees in an office is Rs 150 per month. The average income of officers is Rs 450 and that of Non- officers is Rs 80. If the number of officers is 14. What is the numbers of Non- Officers:- a) 55, b) 60, c) 65, d) 70.
6) In a factory the average weekly income of managers and labors are Rs 400. The average weekly income of managers is 2400. While the average weekly income of labors are 300, find the ratio between the numbers of managers and labors. a) 20:1, b) 1:20, c) 1:21, d) None of these.
7) The average monthly salary of the workers in a workshop in Rs 85. If the average monthly salary of 7 technicians is Rs 10000 and average monthly salary of rest is Rs 7800, the total number of workers in the workshop is:- a) 18, b) 20, c) 22, d) 24.

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