Practice MCQ Questions and Answer on Average

111.

Ajit has a certain average for 9 innings. In the tenth innings, he scores 100 runs thereby increasing his average by 8 runs. His new average is:

(A) 20
(B) 21
(C) 28
(D) 32

Solution: Let Ajit's average be x for 9 innings. So, Ajit scored 9x run in 9 innings. In the 10th inning, he scored 100 runs then average became (x+8). And he scored (x + 8) × 10 runs in 10 innings. Now, $\begin{aligned} \Rightarrow 9 x + 100 = 10 \times (x + 8) \\ or, 9 x + 100 = 10 x + 80 \\ or, x = 100 - 80 \\ or, x = 20 \\ New average = (x + 8) \\ = 28 runs \end{aligned}$

112.

Out of 10 teachers of a school, one teacher retires and in place of him a new teacher 25 years old joins. As a result of it average age of the teachers reduces by 3 years. Age of the retired teacher (in years) is -

(A) 55
(B) 65
(C) 45
(D) 75

113.

The average age of a husband and his wife was 23 years at the times of their marriage. After five years they have a one-year old child. The average age of the family now is-

(A) 19 years
(B) 23 years
(C) 28.5 years
(D) 29.3 years

Solution: Sum of the present ages of husband, wife and child = (23 × 2 + 5 × 2) + 1 = 57 years ∴ Required average = $(\frac{57}{3})$ = 19 years

114.

The average score of a cricketer for ten matches is 38.9 runs. If the average for the first six matches is 42, then find the average for the last four matches.

(A) 33.25
(B) 33.5
(C) 34.25
(D) 35

Solution: Total sum of last 4 matches, = (10 × 38.9) - (6 × 42) = 389 - 252 = 137 Average = $\frac{137}{4}$ = 34.25

115.

The average of n numbers x₁, x₂.....x_n is $\overset{―}{x}$ .Then the value of $\sum_{i = 1}^{n} (x_{i} - \overset{―}{x})$ ÃÂÃÂ is equal to -

(A) n
(B) 0
(C) n $\overset{―}{x}$
(D) $\overset{―}{x}$

Solution: According to the question, Average of 'n' number's x1, x2.....xn is $\overset{―}{x}$ Sum of n numbers = n $\overset{―}{x}$ ∴ $\sum_{i = 1}^{n} (x_{1} - \overset{―}{x})$ Put i = 1, 2, 3.....n then {x1 + x2 + x3 + .....(xn - n $\overset{―}{x}$ )} As we know that x1 + x2 + x3+.....+ xnx = n $\overset{―}{x}$ = (n $\overset{―}{x}$ - n $\overset{―}{x}$ ) = 0

116.

The total number of students in section A and B of a class is 110. The number of students in section A is 10 more than that of section B. The average score of the students in B, in a test, is 20% more than that of students in A. If the average score of all the students in the class is 72, then what is the average score of the students in A?

(A) 66
(B) 68
(C) 63
(D) 70

Solution: A + B = 110 x + 10 + x = 110 x = 50 A = 60 B = 50 $\frac{6 x - 72}{72 - 5 x} = \frac{6}{5}$ (x - 12) × 5 = 72 - 5x 5x - 60 = 72 - 5x 10x = 132 A = 5x = 66

117.

The following table shows the number of working hours and the number of employees employed in a small scale industry

No. of working hours	No. of employees
3 - 5	7
5 - 7	10
7 - 9	18
9 - 11	57
11 - 13	14
13 - 15	8

The average number of working hours of an employee is

(A) 8.5
(B) 9.5
(C) 10.5
(D) None of these

Solution: We have : Mean working hours 4 6 8 10 12 14 No. of employees 7 10 18 57 14 8 Sum of working hours of all the employees = (4 × 7 + 6 × 10 + 8 × 18 + 10 × 57 + 12 × 14 + 14 × 8) = (28 + 60 + 144 + 570 + 168 + 112) = 1082 Total number of employees = (7 + 10 + 18 + 57 + 14 + 8) = 114 ∴ Average number of working hours = $(\frac{1082}{114})$ = 9.49 $\approx$ 9.5

118.

When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?

(A) 57
(B) 56.8
(C) 58.2
(D) 52.2

Solution: Let the average weight of the 59 students be X Therefore, the total weight of the 59 of them will be 59X The questions states that when the weight of this student who left is added, the total weight of the class = 59X + 45 When this student is also included, the average weight decreases by 0.2 kgs 59X + $\frac{45}{60}$ = X - 0.2 => 59X + 45 = 60X - 12 => 45 + 12 = 60X - 59X => X = 57

119.

A batsman makes a score of 270 runs in the 87^th inning and thus increase his average by a certain number of runs that is a whole number. Find the possible values of the new average.

(A) 98
(B) 184
(C) 12
(D) All of these

120.

The average of the ages of Sumit, Krishna and Rishabh is 43 and the average of the ages of Sumit, Rishabh and Rohit is 49. If Rohit is 54 years old, what is KrishnaÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂs age?

(A) 24 years
(B) 36 years
(C) 45 years
(D) Cannot be determined

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