Average

Rule 1 It find the average, when the number of quantities and Aeir sum is given. We have the following formula

Sum of the quantities

a ^ e Number of quantities

ustrative Example l b : A batsman scores 35, 45 and 37 runs in first, second

and third innings respectively. Find the average runs in the three innings.

\Smka: Follow the above formula, we have

35 + 45 + 37 average runs = = 39 runs.

c rcise I Find the average o f first 6 prime numbers.

a)4 b ) 6 - c) 5 - d ) 6 -Find the average o f first 25 multiples o f 5. a) 65 b)60 c)75 d)80 Find the average o f first 5 prime numbers.

[Clerical Grade Exam, 1989] a) 5.6 b)5.5 c)6.5 . d)4.6 Find the average o f first 18 multiples o f 6. a) 75 b)57 c)67 d)76 I f a, b, c, d, e are five consecutive odd integers, then what is their average?

[ B a n k P O Exam, 1989]

abode , -a)a + 4 b) c) 5(a + b + c + d + e) d ) a + 8

What was the average daily expenditure o f a man in 1999 who spent Rs 76535 in the first halfyear and Rs 88165 in the last? a)Rs450 b)Rs451.32 c)Rs451.23 d)Rs 450.23 The average o f first five multiples o f 3 is

[Central Excise & I . Tax, 1988] a)3 b)9 c)12 d) 15

Answers 1. b; Hint: First 6 prime numbers are 2 ,3 ,5 ,7 ,11 and 13.

5(l + 2 + 3 + .... + 25) 2. a; Hint: Required average =

2 5 x 2 6 5 , x = x = 65

2 25

V 1 + 2 + . . . + / J : n{n +1)

3. a; Hint: First five prime numbers are 2 , 3 , 5 , 7 , 1 1 . 4. b 5. a ;Hint :b = a + 2, c = a + 4 , d = a + 6ande = a + 8

.-. required average

a+a+2+a+4+a+6+a+l = a + 4

6. c; Hint: Required average = Rs

7. b

76535 + 88165

365 = Rs451.23

Rule 2 To find the sum, when the number of quantities and their average is given. We have the following formula: Sum of quantities = Average x Number of quantities.

Illustrative Example Ex.: The average marks obtained by 120 candidates in a

certain examination is 35. Find the total marks.

Soln: Following the above formula, we have

the total marks = 120 x 35 = 4200.

Exercise 1. The average weight o f a class having 52 students is 52

kg. Find the total weight o f the class. a) 2504 kg b) 2708 kg c) 2704 kg d) 2407 kg

2. The average scores o f a batsman is 44.4 runs. I f he played 125 innings so far, find the total runs made by him. a) 5550 runs b) 5250 runs c) 5450 runs d) 5560 runs

3. The average marks obtained by 144 candidates in a cer-tain examination is 55. Find the total marks.

178 P R A C T I C E B O O K ON Q U I C K E R MATHS

a) 7290 b)7920 c)7930 d)7390 4. The population o f 6 villages is 803,900,1100,1023,945

and 980. What is the population o f the seventh village i f the average population o f the seven villages is 1000? a) 1249 b)1429 c)1428 d)1349

5. The mean temperature from the 9th to the 16th o f Janu-ary, both days inclusive, was 11.6 C and from the 10th to the 17th i t was 12.2 C. The temperature on the 9th was 10.8 C. What was it on the 17th? a )15 .6C b ) 4 . 8 C c ) 9 . 6 C d ) 1 5 C

6. The weights o f four rowers o f a boat are respectively 70 kg, 72 kg, 73 kg and 74 kg and the average weight o f whole crew, including the coxswain is 70 kg. Find the weight o f the coxswain. a) 61 kg b ) 6 8 k g c ) 6 2 k g d ) 6 3 k g

7. The average weight o f 19 students was 25 kg. By the admission o f a new student the average weight is re-duced to 24.8 kg. The weight o f the new student is a) 24.8 kg b) 20.8 kg c) 20.6 kg d ) 2 1 k g

8. The average o f 6 numbers is 8. What is the 7th number so that average becomes 10? | L I C Exam, 1991] a)22 b) 18 c)21 d)20

9. The average o f 5 0 numbers is 3 8. I f two numbers namely, 45 and 55 are discarded, the average o f remaining num-bers is: [ C B I Exam, 1990] a) 36.50 b) 37.00 c) 37.50 d) 37.52

10. The average age o f an adult class is 40 years. 12 new students with an average age o f 32 years j o i n the class, thereby decreasing the average o f the class by 4 years. The original strength o f the class was:

[Centra l Excise & I . Tax 1989] a) 10 b) 11 c)12 d) 15

11. The average expenditure o f a man for the first five months is Rs 120 and for the next seven months is Rs 130. His monthly average income i f he saves Rs 290 in that year, is: [Railways 1991] a )Rs l60 b ) R s l 7 0 c ) R s l 5 0 d)140

12. The average temperature o f first 3 days is 27 and o f the next 3 days is 29 . I f the average o f the whole week is 28.5 C, the temperature o f the last day is:

[Railways 1991] a)31.5 b)10.5 c ) 2 1 d ) 4 2

13. A cricketer scored 180 runs in the first test and 258 runs in the second. How many runs should he score in the third test so that his average score in the three tests would be 230 runs? [ B a n k P 0 1 9 9 1 ] a)219 b)242 c)334 d) None o f these

14. The average salary o f 20 workers in an office is Rs 1900 per month. I f the manager's salary is added, the average becomes Rs 2000 per month. The manager's annual sal-ary (in Rs) is:

[ S B I P O Exam, 1988] a) 24000 b) 25200 c) 45600 d) None o f these

Answers I . c 2.a 3.b 4. a; Hint: Population o f seventh village = 7 x 1000 - (803 -

900 +1100 +1023 + 945+980) = 1249 5. a; Total temperature from 9th to 16th o f January

= 8x 1 1 . 6 C = 9 2 . 8 C Total temperature from 10th to 17th o f January

= 8 x 12.2 = 97.6 C Now, according to the question, Temperature on 17th o f January

= 10.8 C + 97.6 C - 92.8 C = 15.6 C 6. a; Hint: Required answer = 5 x 70 - (70 + 72 + 73 + 74)

= 61 kg. 7. d; Hint: Weight o f new student = (20 x 24.8 - 19 x 25)

= 21 kg 8. a; Hint: Let 7th number be x.

Sum o f given 6 numbers = (6 x 8) = 48

48 + x

.-. Average o f 7 numbers = ~ .

4 8 + x : . = 1 0 or,48 + x = 70 o rx = 22. Hence, the 7th number is 22.

9. c; Hint: Total o f 50 numbers = 50 x 38 = 1900. Average o f 48 numbers

1900- (45 + 5 5 ) _ 1800 '_.

48 ~ 48

10. c;Hint: 40x + 12x32 = ( l2 + x ) x 3 6 :.X = 12

I I . c 12. a; Hint: Temperature o f the last day

:= [ 2 8 . 5 x 7 - ( 2 7 x 3 ) - ( 2 9 x 3 ) ] = 31.5

13. d; Hint: Let the runs he should score in third test be Then,

= 37.50

180 + 258 + x 230: :252.

14. d; Hint: Total monthly salary o f 21 personnels = Rs (21 x 2000) = Rs 42000.

Total monthly salary o f 20 personnels = Rs(20x 1900) = Rs38000.

Monthly salary o f the manager = Rs 4000.

Annual salary o f the manager = Rs 48000.

Rule 3 To find number of quantities, when the sum of quant? and average are given. We have the following formula:

Sum of quantities Number of quantities =

*' Average

Illustrative Example Ex.: I f the sum o f the ' n ' number o f quantities is 30 and

average is 6. Find the value o f ' n ' .