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Find correct average marks?AVERAGE

1. Average = Sum of observations /Number of observations

2. Number of observations = Sumof observations / Average

3. Sum of observations = Average ×Number of observations

4. If the number of quantities in twogroups be 'm' and 'n', and theiraverages are x and y respectively.Then the average of all of them

put together

5. If the average of m quantities is xand the average of n quantitiesout of them is y, then the average

of remaining group

6. If p is the average of x1, x2, x3,……… xn, thena) The average of x1 + a, x2 + a,x3 + a, ………xn + a is p + ab) The average of x1 – a, x2 – a,x3 – a, ……… xn – a is p – ac) The average of ax1, ax2, ax3,………axn is pa. (If a ≠ 0) d) The average of

7. The average of n quantities isequal to x. When a quantity isremoved, the average becomes y.The value of the removedquantity is n (x – y) + y

8. The average of n quantities isequal to y. When a quantity isadded, the average becomes y.The value of the new quantity isn (y – x) + y

9. The average of first n natural

numbers

10. The average of squares if first n

natural numbers

11. The average of cubes of first n

natural numbers

12. The average of even numbers

from 1 to n

13. The average of first n evennumbers = n + 1

14. The average of odd numbers

from 1 to n

15. The average of first n oddnumbers = n

16. If n is odd: The average of nconsecutive numbers or consecu-tive even numbers or consecutiveodd numbers is always themiddle number.

17. If n is even: The average of n

consecutive numbers or consecu-tive even numbers or consecutiveodd numbers is always theaverage of middle two numbers.

18. The average of squares of first n

even numbers

19. The average of squares of firstconsecutive even numbers till

20. The average of squares of firstconsecutive odd numbers till

21. In cricket, a player's battingaverage is the total number ofruns he has scored divided by thenumber of times he has been out.

22. The average of Arithmetic progr-ession is equal to average of itsfirst and last numbers.

PRACTICE QUESTIONS

1. The total of the ages of a class of75 girls is 1050 years, theaverage age of 25 of them is 12years and that of another 25 is 16years. Find the average of theremaining girls? a) 12 years b) 13 yearsc) 14 years d) 15 yearse) None of these

2. The average monthly income of afamily of four earning memberswas Rs. 15,130. One of thedaughters in the family gotmarried and left home. So theaverage monthly income of thefamily came down to Rs 14,660.What is the monthly income ofthe married daughter?a) Rs. 15,350 b) Rs. 12,000c) Rs. 16,540d) Cannot be determinede) None of these

3. The average age of 30 students ofa class is 14 years. When the ageof the class teacher is included,the average increases 1 year.Find the age of class teacher?a) 25 years b) 30 years c) 32 years d) 36 yearse) None of these

4. In the first 10 overs of a cricketgame, the run rate was only 3.2.What should be the run rate inthe remaining 40 overs to reachthe target of 282 runs?a) 6.25 b) 5.5 c) 5d) 4.75 e) None of these

5. The average of five numbers is27. If one number is excluded,the average becomes 25. What isthe excluded number?a) 40 b) 37 c) 35

d) 30 e) 28.56. The average expenditure of 9

friends out of 10 is Rs. 20. Thetenth friend expenditure is Rs. 45more than the average expendi-ture of all 10 friends. Find thetotal expenditure of all 10friends?a) Rs. 245 b) Rs. 250c) Rs. 255 d) 260e) Cannot be determined

7. The average salary of all the 100workers in a workshop is Rs.24,000. The average salary oftechnicians is Rs. 40,000 and theaverage salary of the rest is Rs.20,000. How many techniciansare there in the workshop?

a) 10 b) 15 c) 18d) 20 e) 26

8. Average weight of 20 peopleincreased by 1.5 kg when oneperson of 50 kg is replaced by anew man. Then find the weightof the new man?a) 51 kg b) 60 kg c) 70 kgd) 75 kg e) 80 kg

9. The average weight of A and B is50 kg; B and C is 70 kg and Cand A is 60 kg. Then find theweight of B?a) 40 kg b) 55 kgc) 58 kg d) 60 kge) Cannot be determined

10. Find the average of 1, 4, 9, 16,……… 625.a) 313 b) 221 c) 216d) 208 e) None of these

11. The average of ten numbers is 7.If each number is multiplied by

12, then the average of the newset of numbers is:a) 7 b) 19 c) 82 d) 84 e) 96

12. Madhu has twice as much moneyas Suresh and Suresh has 50%more money than what Pavanhas. If the average money withthem is Rs 110, then Madhu has a) Rs. 55 b) Rs. 60 c) Rs. 90d) Rs. 180 e) Rs. 220

13. The average marks of 30 studentsin a class are 60. But a studentmarks is wrongly noted as 15instead of 90. Find correctaverage marks?a) 57.5 b) 58.5 c) 62.5 d) 63.5 e) 65

14. If a, b, c, d, e are five consecutiveodd numbers, their average Is:a) 5(a+d) b) 5(a+b+c+d+e)c) abcde d) a+4e) None of these

n(n 2)n

3

+=

(n 1)(n 2)n

3

+ +=

2(n 1)(2n 1)

3

+ +=

n 1

2

+=

n 2

2

+=

2 2n (n 1)

4

+=

(n 1)(2n 1)

6

+ +=

n 1

2

+=

p31 2 n, , ...... isa a a a a

xx x x

m ny

m n

x −=−

m ny

m n

x +=+

B. Ravipal Reddy

Director, SIGMA,

Hyderabad

SBI POs, ClerksQuantitative Aptitude

KEY

1. cTotal age of class of 75 girls = 1050Total age of 25 girls= 25 × 12 = 300Total age of another 25 girls = 25 × 16 = 400So Total age of remaining girls= 1050 – (300 + 400) = 350The average age of remaining

girls

2. cThe total income of the fourfamily members = 4 × 15430 = Rs. 60520Total income of three familymembers = 3 × 14660 = Rs.43980Monthly income of marrieddaughter = 60520 – 43980 = Rs. 16540

3. bThe total age of 30 students = 30 × 14 = 420 yearsThe total age of 31 persons= 30 × 15 = 450 yearsTeachers age = 450 – 420 = 30 years

4. aRuns scored in the first 10 overs= 10 × 3.2 = 32Total runs = 282remaining runs to be scored =282 – 32 = 250remaining overs = 40

Run rate needed

5. cSum of 5 numbers = 5 × 27 = 135Sum of 4 numbers after exclu-

ding one number = 4 × 25 = 100Excluded number = 135 – 100 = 35

6. bLet average expenditure of 10friends = xTenth friend expenditure = x + 45Total expenditure of ten friends= 10x = 9 × 20 + x + 459x = 225 ⇒ x = 25Total expenditure of ten friends= 10x = 10 × 25 = Rs. 250

7. dLet number of technicians = xNumber of other workers= 100 – xTotal salary = 100 × 24000 = x × 40,000 + (100 – x) 2000040000x – 20000x = 40000020000x = 400000 ⇒ x = 20∴ Number of technicians = 20

8. eTotal increased weight= 20 × 1.5 = 30 kgWeight of new person = 50 + 30 = 80 kg

9. dThe total weight of A and B= 2 × 50 = 100 kg

The total weight of B and C = 2 × 70 = 140 kgThe total weight of C and A= 2 × 60 = 120 kg2(A+B+C) = 80 + 120 + 160 = 360A + B + C = 180 kgB's weight = 180 – 120 = 60 kg

10. bThe average of squares of first nnatural numbers

11. dThe average = 12 × 7 = 84

12. dLet Pavan has Rs xthen Suresh has 150% of

Madhu has

Madhu has 3x = 3 × 60 = Rs. 18013. c

According to question totalmarks of 30 students = 30 × 60 = 1800But the correct total marks of30 students = 1800 – 15 + 90 = 1875The correct average marks

Short cut method:The correct average marks =Given average + (Correct marks– Wrong marks) / Num- ber ofstudents

14. dClearly, b = a + 2, c = a + 4,d = a + 6 and e = a + 8. Average

5a 20 5(a 4)(a 4)

5 5

+ += = = +

a a 2 a 4 a 6 a 8

5

+ + + + + + + +=

90 1560 60 2.5 62.5

30

−⎛ ⎞= + = + =⎜ ⎟⎝ ⎠

187562.5

30= =

11330 60

2

xx⇒ = ⇒ =

33 110 3

2

xx+ x⇒ + = ×

32 3

2

xx× =

150 3Rs Rs

100 2

xx x= × =

26 51221

6

×= =

(n 1)(2n 1)

6

+ +=

2506.25

40= =

35014years

25= =

Oòßæ§ýlÆ>»ê§Šl l ÝùÐ]l$ÐéÆý‡… l þ Œæ l 02 l 2014 17ѧýlÅ

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Æ>gê A…MìS±yýl$ ºçßæ§ýl*ÆŠæ H çÜ…Ýë¦

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