Practice MCQ Questions and Answer on Average

141.

There were 24 students in a class. One of them, who was 18 years old, left the class and his place was filled up by a newcomer. If the average of the class thereby, was lowered by one month, the age of the newcomer is-

(A) 14 years
(B) 15 years
(C) 16 years
(D) 17 years

142.

A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreased his average by 0.4. The number of wickets taken by him the last match was-

(A) 64
(B) 72
(C) 80
(D) 85

Solution: Let the number of wickets taken till the last match be x $\begin{aligned} \Rightarrow \frac{12.4 x + 26}{x + 5} = 12 \\ \Rightarrow 12.4 x + 26 = 12 x + 60 \\ \Rightarrow 0.4 x = 34 \\ \Rightarrow x = \frac{34}{0.4} \\ \Rightarrow x = \frac{340}{4} \\ \Rightarrow x = 85 \end{aligned}$

143.

The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?

(A) 13.5
(B) 14
(C) 15
(D) 12.5

Solution: At present the total age of the family = 5 × 20 =100 The total age of the family at the time of the birth of the youngest member, = 100 - 10 - (10 × 4) = 50 Therefore, average age of the family at the time of birth of the youngest member, $= \frac{50}{4} = 12.5$

144.

In a certain factory there are five workers A, B, C, D and E. A can complete a work in 4 minutes, B in 5 minutes, C in 6 minutes, D in 10 minutes and E in 12 minutes. The average number of units of work completed per worker per minute will be-

(A) 0.16
(B) 0.172
(C) 0.80
(D) 0.87

Solution: Number of units of work completed by the five workers in 1 minute: $\begin{aligned} A \to \frac{1}{4}, \\ B \to \frac{1}{5}, \\ C \to \frac{1}{6}, \\ D \to \frac{1}{10}, \\ E \to \frac{1}{12} \end{aligned}$ ∴ Required average $\begin{aligned} = \frac{(\frac{1}{4} + \frac{1}{5} + \frac{1}{6} + \frac{1}{10} + \frac{1}{12})}{5} \\ = (\frac{4}{5} \times \frac{1}{5}) \\ = \frac{4}{25} \\ = 0.16 \end{aligned}$

145.

The sum of the three consecutive even numbers is 44 more than the average of these numbers. Which of the following is the third largest of these numbers?

(A) 16
(B) 18
(C) 24
(D) Cannot be determined

Solution: Let the numbers be x, x + 2 and x + 4 Then, ⇒ (x + x + 2 + x + 4) - $\frac{(x + x + 2 + x + 4)}{3}$ = 44 ⇒ (3x + 6) - $\frac{(3 x + 6)}{3}$ = 44 ⇒ 2 (3x + 6) = 132 ⇒ 6x = 120 ⇒ x = 20 ∴ Largest number = x + 4 = 24

146.

A man started his journey from Lucknow to Kolkata, which is 200 km, at the speed of 40 kmph then he went to Banglore which is 300 km, at the speed of 20 kmph. Further he went to Ahmedabad which is 500 km, at the speed of 10 kmph. The average speed of the man is :

(A) 14 $\frac{2}{7}$ kmph
(B) 14 $\frac{5}{7}$ Kmph
(C) 15.6 kmph
(D) 16.1 kmph

Solution: $\begin{aligned} Average speed, \\ = \frac{Total Distance}{Total time} \\ = \frac{200 + 300 + 500}{\frac{200}{40} + \frac{300}{20} + \frac{500}{10}} \\ = \frac{1000}{70} \\ = 14 \frac{2}{7} kmph \end{aligned}$

147.

The average of 11 players of a cricket team is decreased by 2 months when two of them aged 17 years and 20 years are replaced by two new players. The average age of the new players is-

(A) 17 years 1 month
(B) 17 years 7 months
(C) 17 years 11 months
(D) 18 years 3 months

Solution: Total age decreased = (11 × 2) months = 22 months = 1 year 10 months ∴ Average age of two new players $(\frac{35 years 2 months}{2})$ = 17 years 7 months

148.

The average of 22 number is 52. The average of the first 8 numbers is 48 and the average of next 11 number is 54 the 20^th number is 7 less than the 21^st number and 21^st number is 4 more than 22^nd number. What is the average of the 20^th and 22^nd number?

(A) 52
(B) 52.5
(C) 53
(D) 53.5

149.

Average score of a class of 60 students, in an exam, was 43. Average score of the students who had passed is 52 and the average score of students who had failed is 16. How many failed the exam?

(A) 25
(B) 20
(C) 15
(D) 18

Solution: Total number of students in class = 60 Average score of passed student = 52 Average score of failed students = 16 By applying the rule of alligation, ∴ Number of students who failed in exam = $\frac{1}{4}$ × 60 = 15

150.

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is-

(A) 1 : 2
(B) 2 : 3
(C) 3 : 4
(D) 3 : 5

Solution: Let the ratio be K : 1 Then, ⇔ K × 16.4 + 1 × 15.4 = (K + 1) × 15.8 ⇔ (16.4 - 15.8) K = (15.8 - 15.4) ⇔ K = $\frac{0.4}{0.6}$ ⇔ K = $\frac{2}{3}$ ∴ Required ratio = $\frac{2}{3}$ : 1 = 2 : 3

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