Average problems
- 1. The average weight of a class of 15 boys and 10 girls is 38.4 kg. If the average weight of the boys is 40 kg, then what is the average weight of the girls?
Options- A. 36.5 kg
- B. 35 kg
- C. 36 kg
- D. 35.6 kg Discuss
Correct Answer: 36 kg
Explanation:
Given that, number of boys (n1) = 15
Numbers of girls (n2)= 10
Average weight of boys and girls = 38.4 kg
Average of boys = 40 kg
Let average of girls be a2
By formula, average = (na1 + n2 a2) / (n1 + n2)
? 38.4 = (15(40) + 10 x a2)/(15 + 10)
? 38.4 x 25 = 600+ 10a2
? a2= (960 - 600)/10 = 360/10 = 36 kg
- 2. The average marks of 120 students are 35. if the average of passed stuydents was 39. and failed students was 15 then find the number of students who have passed
Options- A. 80
- B. 100
- C. 120
- D. 140 Discuss
Correct Answer: 100
Explanation:
Here n = 120, a = 35, x = 39, y = 15
Number of students passed = n (a - y)/(x - y)
= 120(35 - 15)/(39 -15)
= 100 students passed
- 3. A car travels a certain distance from town A to town B at the speed of 42 km/h and from town B to town A at a speed of 48 km/h. What is the average speed of the car?
Options- A. 45 km/h
- B. 46 km/h
- C. 44 km/h
- D. Cannot be determind Discuss
Correct Answer:
Explanation:
If two equal distance are covered at different speeds at A km/h and B km/h respectively, then
Average speed during the whole journey = 2AB/(A + B) km/h
? Average speed of the car = (2 x 42 x 48) / (42 + 48)
= (2 x 42 x 48)/90
= 44.8 km/h
- 4. The average of four positive integers is 73.5. The highest integer is 108 and the lowest integer is 29, the difference between the remaining two integers is 15. Which of the following is the smaller of the remaining two integers?
Options- A. 80
- B. 86
- C. 73
- D. Cannot be determind Discuss
Correct Answer:
Explanation:
Let one integer be x.
? Other ingeger x + 15
According to the question,
29 + x + x + 15+ 108 = 4 x 73.5
? 2x + 152 = 294
? 2x = 294 - 152 = 142
? x = 142/2 = 71
- 5. A cricketer scored some runs in his continuous 9 innings. He scored 100 runs in his 10th innings and increase his average by 8 runs. What was the average of his runs at the end of 10 th innings?
Options- A. 20
- B. 24
- C. 28
- D. 32 Discuss
Correct Answer: 28
Explanation:
Let average of a inning = x
Total runs = 9x
According to the question,
(9x + 100) /10 = x + 8
? 9x + 100 = 10x + 80
x = 20
Average after 10 inning = 20 + 8 = 28
- 6. Three year ago, the average age of a family of five members was 27 yr. The present average age is also 27 yr after the inclusion of a child into the family. Find the age of the child.
Options- A. 16 yr
- B. 12 yr
- C. 24 yr
- D. 20 yr. Discuss
Correct Answer: 12 yr
Explanation:
Total age of 5 memeber (3 yr ago) = 27 x 5 = 135 yr
Total age of 5 members (at present) = 135 + 5 x 3 = 150 yr.
Let the persent age of child = x
? 27 = (150 + x)/6
? x = 162 - 150 = 12 yr.
- 7. The average age of three boys is 15 yr. If the ratio of their ages is 3 : 5 : 7, What is the age of the oldest boy?
Options- A. 7 yr
- B. 14 yr
- C. 20 yr
- D. 21 yr Discuss
Correct Answer: 21 yr
Explanation:
Total age of all three boys
= 3 x 15 = 45 yr
Ratio of ages = 3 : 5 : 7
? Age of the oldest boy
= [7/(3 + 5 + 7)] x 45 = (7/15) x 45 = 21 yr
- 8. Nine friends have dinner in a hostel. Eight of them spent ? 12 each on their meals and the ninth spent ? 16 more than the average expenditure of all the nine. Find out the total money spent by them?
Options- A. ? 126
- B. ? 135
- C. ? 111
- D. ? 141 Discuss
Correct Answer: ? 126
Explanation:
Let average expenditure of 9 persons = x.
According to the question,
12 x 8 + (x + 16) = 9x
? 8x = 112
? x = 112/8 = 14
? Total money spent = 9x = 9 x 14 = ? 126
- 9. In a certain examination, the average marks of an examinee is 64 per paper. if he had obtained 18 more marks for his Mathematics paper and 4 more marks for his English paper, his average per paper would have been 66. How many papers were there in the examination?
Options- A. 11
- B. 13
- C. 9
- D. 15 Discuss
Correct Answer: 11
Explanation:
Let the number of papers = x.
According to the question,
64x + 18 + 4 = 66x
? 2x = 22
? x = 22/2 = 11
- 10. The average markes obtained by 120 students in an examination is 30. if the aveage marks of passed students is 40 and that of the failed students is 10. what is the 25% of the number of students who passed the examination?
Options- A. 30
- B. 20
- C. 40
- D. 15 Discuss
Correct Answer: 20
Explanation:
Let number of passed students = N
Total marks = 120 x 30
According to the question,
40N + (120 - N) x 10 = 120 x 30
? 3600 = 40N + 1200 - 10N
? 30N = 2400
? N = 2400/30 = 80
? 25% of 80 = 80/4 = 20
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