Average problems
- 1. Columbus started his journey from Lucknow to Kolkata, Which is 200 K.M., at the speed of 40 KM/hr, then he went to Banglore which is 300 Km, at the speed of 20 KM/hr . Further he went to Ahmedabad which is 500 Km, at the speed of 10 Km/hr. The average speed of Columbus is :
Options- A. 14 2/7 KM/hr
- B. 14 5/7 KM/hr
- C. 15.6 KM/hr
- D. none of these Discuss
Correct Answer: 14 2/7 KM/hr
Explanation:
Total distance = (200 + 300 + 500) = 1000
Total time = 200/40 + 300/20 + 500/10 = 5 + 15 + 50 = 70 hr
Average speed = Total distance / Total time =1000 / 70 = 14.2857 Km/hr.
- 2. If the algebraic sum of deviations of 20 observation measured from 23 is 70, mean of these observation would be
Options- A. 24
- B. 25
- C. 26
- D. 27 Discuss
Correct Answer:
Explanation:
Mean = (sum of observation) / (number of observation)
Sum of observation is given as = 70
Number of observation = 20
? Mean = 70/20 = 3.5
But, here observation starts from= 23.
? Mean = 23 + 3.5 = 26.5
- 3. The average of 50 number is 38. If the two numbers 45 and 55 are not considered, What will be the average of remaining numbers?
Options- A. 36.5
- B. 37
- C. 37.5
- D. 37.52 Discuss
Correct Answer: 37.5
Explanation:
According to the basic formula of average,
Average(A)= Sum (S) / Number(N)
? 38 = S/50
? S = 38 x 50 = 1900
Sum of remaining number after eliminating 45 and 55
= 1900 - (45 + 55) = 1800
Average of remaining numbers = (Sum of remaining number) / (Remaining number)
= 1800 / ( 50 - 2)
= 1800/48
= 37.5
- 4. The average marks of 30 students are 45 but after checking there are two mistakes found. After adjustment if a student got 45 more markes and other student got 15 less marks, then What will be the adjusted average?
Options- A. 45
- B. 44
- C. 47
- D. 46 Discuss
Correct Answer: 44
Explanation:
Total number of all students of the class = 30 x 45 = 1350
? New average after adjustment = (1350 - 45 + 15)/30 = 1320/30 = 44
- 5. The mean marks obtained by seven students group is 226. If the marks obtained by six of them are 340, 180, 260, 56, 275 and 307 respectively. Find the markes obtained by the seventh student.
Options- A. 164
- B. 226
- C. 340
- D. cannot be determined Discuss
Correct Answer: 164
Explanation:
Sum of marks of 7 students = Mean x Number of students
= 226 x 7 = 1582
Now, total marks of 6 students = (340 + 180 + 260 + 56 + 275 + 307) = 1418
? Marks obtained by seventh students
= Total marks of seven students - Total marks of the six student
= 1582 - 1418
= 164
- 6. The average age of 4 member of a family is 25 yr. If head of the family is included in this group then average age increase by 20%. Find out the age of the head.
Options- A. 45 yr
- B. 50 yr
- C. 55 yr
- D. 60 yr Discuss
Correct Answer: 50 yr
Explanation:
Total age of 4 member = 25 x 4 = 100 yr
Total age of 5 members including the head
= 5 x (25 + 25 x 20/100)
= 5 x 30 = 150 yr
? Age of the head = 150 - 100 = 50 yr
- 7. The average age of a committee of 11 persons increases by 2 yr when 3 men of 32 yr. 34 yr and 33 yr are replaced by 3 woman. What will be the average age of those 3 woman?
Options- A. 40 yr
- B. 411/3 yr
- C. 41 yr
- D. 401/3 yr Discuss
Correct Answer: 401/3 yr
Explanation:
Total age of 3 woman = 2 X 11 + (32 + 33 + 34)
= 22 + 99 = 121 yr.
? Average age of 3 woman = 121/3 = 401/3 yr
- 8. The average weight of 10 woman is incraesed by 1 kg if 2 woman of 42 kg and 38 kg are replaced by 2 men.Find the average weight of both the men?
Options- A. 46 kg
- B. 45kg
- C. 42 kg
- D. 44 kg Discuss
Correct Answer: 45kg
Explanation:
Total weight of 2 men
= 1 x 10 + (42 + 38) = 10 + 80 = 90 kg
? Average weight of 2 men = 90/2 = 45 kg
- 9. The mean weight of 150 students in class is 60 kg. The mean weight of boys is 70 kg and that of girls is 55 kg. What is the number of boys in the class?
Options- A. 50
- B. 60
- C. 75
- D. 100 Discuss
Correct Answer: 50
Explanation:
Given that total number of students = 150 = ( n1+ n2) and
Mean weight of 150 students = 60 kg.
The mean weight of boys a1= 70 kg and
The mean weight of girls a2 = 55 kg
Let n1 and n2 be the number of boys and girl, respectively.
? n1 + n2 = 150 ...(i)
11 n1 + 11 n2 = 1650 ...(ii)
Average weight = (n1 a1 + n2 a2) / (n1 + n2)
? 60 = (70 n1 + 55n2)/150
? 70 n1 + 55n2 = 9000
? 14n1 + 11n2 =1800 ...(iii)
On subtracting Eq. (ii) from Eq. (iii), we get
3n1 = 150 ? n1 = 50
Hence, required number of boys is 50.
- 10. The average monthly income of 4 earning members of a family is ? 7350. One member passes away and the average monthly income become ? 6500. What was the monthly income of the person, who is no more?
Options- A. ? 6928
- B. ? 8200
- C. ? 9900
- D. ? 13850 Discuss
Correct Answer: ? 9900
Explanation:
Monthly income of 4 persons = 7350 x 4 = ? 29400
Monthly income of 3 person (excluding the dead person) = 6500 x 3 = ? 19500
? Monthly income of dead person = 29400 - 19500 = ? 9900
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