Average problems
- 1. P, Q, R, S, T and U are six consecutive odd numbers and their average is 52. What is the product of P and U ?
Options- A. 2212
- B. 2154
- C. 2349
- D. 2679 Discuss
Correct Answer: 2679
Explanation:
Let x, x+2, x+4, x+6, x+8 and x+10 are six consecutive odd numbers.
Given that their average is 52
Then, x + x+2 + x+4 + x+6 + x+8 + x+10 = 52×6
6x + 30 = 312
x = 47
So Product = 47 × 57 = 2679
- 2. In a class of 78 students 41 are taking French, 22 are taking German. Of the students taking French or German, 9 are taking both courses. How many students are not enrolled in either course?
Options- A. 6
- B. 12
- C. 24
- D. 18 Discuss
Correct Answer: 24
Explanation:
You could solve this by drawing a Venn diagram. A simpler way is to realize that you can subtract the number of students taking both languages from the numbers taking French to find the number taking only French. Likewise find those taking only German. Then we have:Total = only French + only German + both + neither
78 = (41-9) + (22-9) + 9 + neither.
Not enrolled students = 24
- 3. The average of 9 results is 50. The average of the first four results is 52 and the average of the last four results is 49. what is the fifth result?
Options- A. 48
- B. 46
- C. 52
- D. 44 Discuss
Correct Answer: 46
Explanation:
Total of first four results = 52 x 4 = 208
Total of Last four results = 49 x 4 = 196
Hence the fifth result = 450 - (208 + 196) = 46
- 4. The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is :
Options- A. 6000
- B. 7000
- C. 8888
- D. 9000 Discuss
Correct Answer: 9000
Explanation:
Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.
Cost of cheapest item = 3x = Rs. 9000.
- 5. In a mens hostel, there were 95 students. To accommodate 30 more students the average is decreased by rupees 5. But total expenditure increased by Rs.500. Find the total expenditure of the hostel now ?
Options- A. Rs. 4680
- B. Rs. 4420
- C. Rs. 4960
- D. Rs. 5480 Discuss
Correct Answer: Rs. 4680
Explanation:
Let the expenditure on the 95 students be 'x'
Then,
95x + 500 = 120(x ? 5)
95x + 500 = 120x - 600
120x - 95x = 1100
25x = 1100
=> x = 44
Therefore, total expenditure of the hostel becomes
95 x 44 + 500 = 4680.
- 6. David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Mathematics,Physics, Chemistry and Biology What are his average marks ?
Options- A. 75
- B. 68
- C. 65
- D. 60 Discuss
Correct Answer: 75
Explanation:
Average = (76 + 65 + 82 + 67 + 85 )/ 5 = 375/5 = 75.
- 7. The mean of 100 observations is 40. It is found that an observation 84 was misread as 48. Then the correct mean is ?
Options- A. 40.36
- B. 41.24
- C. 41.92
- D. 42.05 Discuss
Correct Answer: 40.36
Explanation:
Given,
mean of 100 observations is 40
=> Total of 100 observations = 40 x 100 = 4000
84 is misread as 48
=> Difference = 84 - 48 = 36
=> Now, new total of 100 observations = 4000 + 36 = 4036
Correct Mean = 4036/100 = 40.36
- 8. Without any stoppage, a person travels a certain distance at an average speed of 42 km/h, and with stoppages he covers the same distance at an average speed of 28 km/h. How many minutes per hour does he stop?
Options- A. 15 minutes
- B. 20 minutes
- C. 18 minutes
- D. 22 minutes Discuss
Correct Answer: 20 minutes
Explanation:
Let the total distance to be covered is 84 kms.
Time taken to cover the distance without stoppage = 84/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 84/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.
- 9. The average age of 7 boys is increased by 1 year when one of tem whose age is replaced by a girl. What is the age of the girl ?
Options- A. 33 yrs
- B. 27 yrs
- C. 21 yrs
- D. 29 yrs Discuss
Correct Answer: 29 yrs
Explanation:
Let the avg age of 7 boys be 'p' years
Let the age of the girl be 'q' years
From given data,
The age of 7 boys = 7p years
Now the new average = (p + 1) when 22 yrs is replaced by q
Now the age of all 7 will become = 7(p + 1) yrs
Hence, 7p - 22 + q = 7(p + 1) yrs
7p - 22 + q = 7p + 7
q = 22 + 7 = 29
Therefore, the age of girl = q = 29 years.
- 10. In Arun's opinion, his weight is greater than 65 kg but leas than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of diferent probable weights of Arun ?
Options- A. 55.5 kg
- B. 66.5 kg
- C. 77.5 kg
- D. 88.5 kg Discuss
Correct Answer: 66.5 kg
Explanation:
Let Arun's weight be X kg.
According to Arun, 65 < X < 72.
According to Arun's brother, 60 < X < 70.
According to Arun's mother, X < 68.
The values satisfying all the above conditions are 66 and 67.
Required average = (66 + 67) / 2 = 66.5 kg
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