Average

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31.

The average weight of 8 persons increases by 1.5 kg. If a person weighing 65kg is replaced by a new person, what could be the weight of the new persons?

80 kg

73 kg

77 kg

83 kg

View Answer

Shortcut: The weight of new persons is (b + na) that means: Weight of new persons = Weight of removed person + No. of persons x Increase in average Here, n=8, a=1.5, b = 65 Using these values in shortcut, we get 65 + 8x1.5 = 65+12 = 77 Hence, the average weight of new person = 77 years

32.

The average age of a committee of 7 trustees is the same as it was 5 years ago, a younger man having been substituted for one of them. How much younger was he than the trustee whose place he took?

39 years

42 years

31 years

35 years

View Answer

The average age of committee of 7 trustees is same as it was 5 years ago. But today committee gains 7 x 5 = 35 years. Hence, we can conclude that the youngest man who replaced the trustee 5 years ago is 35 years younger than the trustee whose place he took. Let 7 trustee are a,b,c,d,e,f and g 5 years ago, their average age =

a+b+c+d+e+f+g / 7

Let one of them 'a' is replaced by 'z', then today their average age

(z+5)+(b+5)+(c+5)+(d+5)+(e+5)+(f+5)+(g+5) / 7

(z+b+c+d+e+f+g)+35 / 7

Now, the question says that the average age is same as it was 5 years ago, which could be possible if we remove 35 from eq (3). ∴ new member is 35 years younger than the trustee whose place he took.

33.	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 the new boy.
	A.	14 years 8 months
	B.	12 years 4 months
	C.	13 years 2 months
	D.	11 years 9 months

		View Answer Shortcut: The average age of 'n' persons is decreased by 'a' years when some of them aged 'b' are replaced by the same number of persons. Then the age of the new persons is [b-na] i.e Age of new persons= Age of removed persons - No. of persons x Decreased in average here, n=20, a=2 months b=18 using these values in shortcut, we get 18 - 20 x 2 / 12 = 18 - 10 / 3 = 14 2 / 3 = 14 years 8 months

34.	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 candiates is 15, what is the number of candidates who passed the examination?
	A.	110
	B.	100
	C.	90
	D.	105

		View Answer The average of marks obtained by 'n' candidates in a certain examination is 'A'. If the average marks of passed candidates is 'P' and that of the failed candidates is 'F'. Then the number of candidates who passed the examination is n(A-F) / P-F i.e Number of passed candidates = Total candidates(Total Average - Failed Average) / Passed Average - Failed Average n=120 A=35 P=39 F=15 Using these values in shortcut, we get 120(35-15) / 39-15 = 120 x 20 / 24 = 100

35.

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 failed the examination?

View Answer

Shortcut: The average of marks obtained by 'n' candidates in a certain examination is 'A'. If the average marks of passed candidates is 'P' and that of the failed candiadates is 'F'. Then the number of candidates who failed the examination is

n(P-A) / P-F

i.e Number of failed candidates =

Total candidates(Passed average - Total Average) / Passed Average - Failed Average

Here, n = 120, A = 35, P = 39, F = 15
Using these values in shortcut, we get

120(39-35) / 39-15

120 x 4 / 24

= 20

36.

The average of 11 results is 50. If the average of first six results is 49 and that of last six is 52, find the sixth result.

View Answer

Shortcut: If the average of n (let n=odd number) results is 'q' and the average of first

n+1 / 2

result is 'r' and that of last

n+1 / 2

is 't'.
Then

n+1 / 2

th result is

n+1 / 2

(r+t) - nq
Here, n = 11, q = 50, r = 49 and t = 52
Using these values in shortcut, we get:
Sixth result =

11+1 / 2

(49+52) - 11 x 50 = 6 x (101) - 550 = 56

37.

The average of 11 results is 30, that of the first five si 25 and that of the last five is 28. Find the value of the 6th number.

View Answer

Value of 6th number = Total sum of 11 results - (Total sum of first five + Total sum of last five results)
= (11 x 30) - ( 5 x 25 + 5 x 28 ) = 330 - 265 = 65

38.

A batsman in his 17th innings makes a score of 85 and thereby increases his average by 3. what is his average after 17 innings?

View Answer

Shortcut: If a batsman in his nth innings makes a score of 'a' and thereby increases his average by 'b', then the average after 'n' inning is [a - b(n - 1)]
Here, n=17, a = 85, b=3
Using these values in shortcut, we get
Average after 17 innings = [a - b(n - 1)] = [85 - 3(17 - 1)] = 85 - 48 = 37

39.

A cricketer has completed 10 innings and his average is 21.5 runs. How many runs must he make in his next innings so as to raise his average to 24?

View Answer

Shortcut:
If a cricketer has completed 'n' innings and his average is 'a' runs. The number of runs, he must make in his next innings so as to raise his average to 'b' are
[n(b - a) + b]
Here, n = 10, b = 24, a = 21.5
10(24 - 21.5) + 24 = 25 + 24 = 49

40.

A train travels from A to B at the rate of 20 km hour and from B to A at the rate of 30 km per hour. What is the average rate for the whole journey?

25 km/hr

20 km/hr

24 km/hr

26 km/hr

View Answer

Shortcut:
If a person travels a distance at a speed of a km/hr and the same distance at a speed of b km/hr. then the average speed during the whole journey is

2ab / a+b

It can be written as:

If half of the journey is travelled at a speed of a km/hr and the next half at a speed of b km/hr, then average speed during the whole journey is

2ab / a+b

Here, a = 20 km/hr, b = 30 km/hr
Using these values in shortcut, we get

2 x 20 x 30 / 20 + 30

2 x 20 x 30 / 50

= 2x4x3 = 24

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