Practice MCQ Questions and Answer on Average

91.

The arithmetic mean of the scores of a group of students in a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25% a mean score of 31. The mean score of remaining 55% is-

(A) 45
(B) 50
(C) 51.4 approx
(D) 54.6 approx

Solution: Let the required mean score be x Then, $\begin{aligned} 20 \times 80 + 25 \times 31 + 55 \times x = 52 \times 100 \\ \Leftrightarrow 1600 + 775 + 55 x = 5200 \\ \Leftrightarrow 55 x = 2825 \\ \Leftrightarrow x = \frac{2825}{55} \approx 51.4 \end{aligned}$

92.

The mean of 20 items is 55. If two items 45 and 30 are removed, the new mean of the remaining items is :

(A) 65.1
(B) 65.3
(C) 56.9
(D) 56

Solution: According to the question, Mean of 20 items is = 55 Sum of 20 items is = 55 × 20 = 1100 Two items removed= 45 + 30 = 75 Now, sum of 18 items= 1100 - 75= 1025 ∴ Average = $\frac{1025}{18}$ = 56.9

93.

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is Rs. 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

(A) 3500
(B) 4000
(C) 4050
(D) 5000

94.

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:

(A) 250
(B) 276
(C) 280
(D) 285

Solution: Since the month begins with a Sunday, to there will be five Sundays in the month. $\begin{aligned} ∴ Required average \\ = \frac{510 \times 5 + 240 \times 25}{30} \\ = \frac{8550}{30} \\ = 285 \end{aligned}$

95.

Find the average increase rate, if increase in the population in the first year is 30% and that in the second year is 40%.

(A) 41%
(B) 56%
(C) 40%
(D) 38%

Solution: Let 100 be the original population. 1st year's population increased = 30% So, Population after first year = (100 + 30% of 100) = 130 Population in second year increases by 40%, Then Population = (130 + 40% of 130) = 182 The final population become 182 which was originally at 100. It means there is 82% increment in the population in 2 years So, Average increment = $\frac{82}{2}$ = 41% Mind Calculation Method: Increase in population is given by, 100 == 30% $↑$ ⇒ 130 == 40% $↑$ ⇒ 182 Hence, average increase = $\frac{82}{2}$ = 41%

96.

If the average of x and $\frac{1}{x}$ (x $\neq$ 0) is M, then the average of x² and $\frac{1}{x^{2}}$ is :

(A) 1 - M2
(B) 1 - 2M2
(C) 2M2 - 1
(D) 2M2 + 1

Solution: According to the question, Average of $\frac{x + \frac{1}{x}}{2} = M$ Put x = 1 $\begin{aligned} ∴ \frac{1 + \frac{1}{1}}{2} = M \\ \Rightarrow M = 1 \\ ∴ \frac{x^{2} + \frac{1}{x^{2}}}{2} \\ = \frac{1^{2} + \frac{1}{1^{2}}}{2} \\ = 1 \end{aligned}$ Now check from the option Option: (C) 2M2 - 1 (put M = 1) = 2 × 1 - 1 = 1 (satisfied) Alternate : According to the question, $\begin{aligned} \Rightarrow \frac{x + \frac{1}{x}}{2} = M \\ Squaring the both sides \\ \Rightarrow x^{2} + \frac{1}{x^{2}} = (2 M)^{2} - 2 \\ \Rightarrow x^{2} + \frac{1}{x^{2}} = 4 M^{2} - 2 \end{aligned}$ Required average $\begin{aligned} = \frac{x^{2} + \frac{1}{x^{2}}}{2} \\ = \frac{4 M^{2} - 2}{2} \\ = 2 M^{2} - 1 \end{aligned}$

97.

The average price of 10 books is Rs.12 while the average price of 8 of these books is Rs.11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?

(A) Rs. 5, Rs.7.50
(B) Rs. 8, Rs. 12
(C) Rs. 16, Rs. 10
(D) Rs. 12, Rs. 14

Solution: Total cost of 10 books = Rs. 120 Total cost of 8 books = Rs. 94 ⇒ The cost of 2 books = Rs. 26 Let the price of each book be x and y. ⇒ x + y = 26 - - - - - - (1) $(\frac{160}{100}) x + y = 26$ On Solving for y, we get y = 10 Now, Substituting y = 10 in (1) we get, x + 10 = 26 x = 16 So the price of each book is Rs. 16 and Rs. 10 respectively.

98.

The average of marks in Mathematics for 5 students was found to do 50. Later, it was discovered that in the case of one student the marks 48 were misread as 84. The correct average is :

(A) 40.2
(B) 40.8
(C) 42.8
(D) 48.2

Solution: According to the question, Correct average $\begin{aligned} = \frac{5 \times 50 + 48 - 84}{5} \\ = \frac{250 - 36}{5} \\ = \frac{214}{5} \end{aligned}$ = 42.8

99.

The average weight of 21 boys was recorded as 64 kg. If the weight of the teacher was added, the average increased by 1 kg. What was the teacherÃÂÃÂÃÂÃÂ¢ÃÂÃÂÃÂÃÂs weight?

(A) 86 kg
(B) 64 kg
(C) 72 kg
(D) 84 kg

100.

The average weight of boys in a class is 30 kg and the average weight of girls in the same class is 20 kg. If the average weight of the whole class is 23.25 kg, what could be the possible strength of boys and girls respectively in the same class?

(A) 14 and 26
(B) 13 and 27
(C) 17 and 17
(D) None of these

Solution: Let the number of boys and girls in the class are x and y. According to given information, ⇒ 30x + 20y = 23.25 (x + y) ⇒ 30x + 20 y = 23.25x + 23.25y ⇒ 30x - 23.25x = 23.25y - 20y ⇒ 6.75x = 3.25y ⇒ $\frac{x}{y}$ = $\frac{3.25}{6.75}$ ⇒ $\frac{x}{y}$ = $\frac{13}{27}$ Hence, possible number of boys and girls 13 and 27 respectively.

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Practice MCQ Questions and Answer on Average

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