# QUEST FOR QUANTITY :: PROBLEMS ON AVERAGES FOR IBPS CLERK MAINS EXAM

**Average**

An average or an arithmetic mean of given data is the
sum of the given observations divided by number of observations.

**Average (A) = (Sum of given observations) (s)/ Number of observations**

**Some Important Concepts:**

1.Average =total observation /No.of observations

2.If the value of each item is increase by the same
value a, then the average of

the group or items will also increase by a.

3.If the value of each item is decreased by the same
value a, then the aveage of the group of items will also decrease by a.

4.If the value of each item is multiplied by the same
value a, then the average

of the group or items will also get multiplied by a.

5.If the value of each item is multiplied by the same
value a, then the average of the group or items will also get divided by a.

6.If we know only the average of the two groups
individually, we cannot find out the average of the combined group of items.

7.Average of n natural no's=(n+1)/2

8.Average of even No'=(n+1)

9.Average of odd No'= n

10.General Formula=(1st number +Last number)/2

11. Average of ‘1 to n’ odd numbers = Last odd number
+1/2.

12. Average of ‘1 to n’ even numbers = Last evennumber
+2/2.

13. Average of squares of first ‘n’ natural numbers =
(n+1) (2n+1)/6.

14. Average of cubes of first ‘n’ natural numbers = n
(n+1)2 /4.

15. Average of ‘n’ multiples of any numbers
= Number X (n+1) / 2.

**Question based on average:**

1.The average age of 30 students is 9 yrs. If the age of
the teacher is include, the average age becomes 10 yrs. What is the age of teacher?

A. 27 yr

B.31 yr

C. 35 yr

D.40 yr

E. none of these

2.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.

(a)48

(b)36

(c)42

(d)29

(e)none of these

3.In a class, there are 20 boys whose average age is
decreased by 2 months, when one boy aged 18 years is replaced by a new boy.Find
the age of new boy.

(a)19 years

(b)14 years 6 month

(c)15 years

(d)14 years 8 month

(e)12 years

4.One -third of certain journey is covered at the rate
of 25kmph,one-fourth at the rate of 30kmph and the rest at 50 kmph.Find the
average speed for the whole journey.

(a)33.33 kmph

(b)36

(c)42

(d)27

(e)none of these

5.The average salary of the entire staff in a office is
Rs 120 per month.The average salary of officers is Rs 460 and of non officers
is Rs 110. If the number of officers is 15,then find the No of non-officers in
the office.

(a)480

(b)500

(c)600

(d)430

(e)510

6.There were 35 students in a hostel.If the number of
students increased by 7, the expenses of the mess increases by Rs. 42 per
day,while the average expenditure per head diminishes by Rs.1.Find the original
expenditure of the mess.

(a)420

(b)400

(c)480

(d)460

(e)none of these

7.The average weight of A,B,and 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 3 kg more than D Replaces A, Then the average of B,C,Dand E becomes
79 kg. What is the weight of A?

(a)64

(b)72

(c)75

(d)100

(e)80

8.In an exam, the average was found to be 50 marks.
After deducting computational errors the marks of the 100 candidates had to be
changed from 90 to 60 each and average came down to 45 marks. Total No of candidates who took
the exam were.

(a)300

(b)600

(c)200

(d)150

(e)none of these

9. Find the average of all even No's up to 100 or
average of first 50 even No's.

(a)50

(b)50.5

(c)51

(d)49

(e)none of these

10. The average of 8 No's is 20. The average of first
two No's is 15.5 and that of next three No's is 64/3.if the 6th No be less than
the seventh and eight No. by 4 and 7 respectively, then find eight No.

(a)26

(b)25.5

(c)27

(d)25

(e)none of these

**Answers with Explanation:**

1. age of teacher = n (b-a) + b.

Where n = 30

Initial
average a =9.

Last average
b = 10.

Required age =
30(10-9) + 10

=
30+10 = 40 years.

2.(a) Total increase = 8 * 2 = 16 years

So, total age of two women = 35 + 45 +16= 96

Average age of two women=96/2=48 years

3.(d) Total decrease = 20 * 2 = 40 month

= 3 years 4 month

So, age of new boy
= 18 years – 3 years 4 month

= 14 years 8 month

4.(a) Average speed = total distance / total time

LCM = 3, 4 = 12

Average speed = 12 / (1/3*12*1/25 + ¼ * 12*1/30 +5/50)

= 12/ (4/25 + 3/30+ 5/30

= 150*12/54 = 33.333 kmph

5.(e) Let no. of non- officers be x

15 * 460 + x * 110 = (x + 15) 120

x = 510

6.(a) Let average expenditure per head be = x

So, (35 + 7) (x -1) – 35 x = 42

42 (x -1) – 35x = 42

X =12

Original expenditure of mess = 12 * 35 = 420

7.A + B + C = 3 *84 = 252

A + B + C + D = 4 * 80 = 320 ---- (i)

So, D = 68&
E = 68 + 3 = 71

B + C + D +E = 79 * 4 = 316 --- (ii)

From Eq. (i) & (ii)

A-E = 320 – 316 = 4

A = E +4 = 71 + 4 = 75

8.(b) Let the total no. of candidates = x

So, (50x-100 (90-60)) / x = 45

x = 600

9.(c) 2, 4, 6, ………… 100

Average = (1st No. + Last No.) /2 = (2+100)/2 = 51

10.(c) Total Sum of 8 nos. = 20 * 8 = 160

Sum of 1st two nos. = 2 * 15.5 = 31

Sum of next three nos. = 3 * 64/3 = 64

Let 6th no. be x

31 + 64 + x +
(x+4) + (x+7) = 160

x = 18

8th no. = 18 + 7 = 25

QUEST FOR QUANTITY :: PROBLEMS ON AVERAGES FOR IBPS CLERK MAINS EXAM
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