1. The average of 12 numbers is 24. If each number be multiplied by 6. Find the average of new set of numbers?
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Correct Ans:144
Explanation:
New Average = Old Average x 6 = 24 x 6 = 144
2. The average of 22 numbers is zero. Of them, at the most how many may be greater than zero?
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Correct Ans:21
Explanation:
W.K.T, Average of 22 numbers = Sumof 22 numbers / 22
Given, Average of 22 numbers = 0.
Therefore sum of all 22 numbers = (0 X 22) = 0.
It is quite possible that21 of these numbers may be positive (greater than 0)and if their sum is "a" then 22nd number is "(-a)".
Alternate Solution:
Now for the sum of 22 numbers to be equal to zero, there may be all 21 numbers of them >0 and only one number which is -ve of all the 21 numbers sum.
3. In the first 30 overs of a cricket game, the run rate was only 8.2. What should be the run rate in the remaining 20 overs to reach the target of 289 runs?
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Correct Ans:2.15
Explanation:
Required Run rate = ( 289 - ( 8.2 x 30 ) )/ (20)
= ( 43) /(20) = 2.15
4. The average temperature for Monday, Tuesday and Wednesday is 36.3^{0} C. The average temperature for Tuesday, Wednesday and Thursday is 36.7^{0} C. If Monday's temperature recorded as 39^{0} C, find the Thursday's temperature ?
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Correct Ans:40.2^{0} C
Explanation:
Mon + Tue + Wed Temperature = 3X36.3 = 108.9
Given, Monday's temperature = 39^{0} C
=> Tue + wed Temperature = 108.9 - 39 = 69.9
Given, Tue + wed + Thu temperature = 3 X 36.7 = 110.1
So, Thursday's temperature = 110.1 - 69.9 = 40.2^{0} C
5. The average of 20 numbers is zero. Of them, at the most how many may be greater than zero?
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Correct Ans:19
Explanation:
Average of 20 numbers is = 0
Therefore sum of all 20 numbers = 0
It is quite possible that 19 of these numbers may be positive and if their sum is "a" then 20th number is "(-a)"
6. In the first 30 overs of a cricket game, the run rate was only 5.4. What should be the run rate in the remaining 20 overs to reach the target of 314 runs?
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Correct Ans:7.6
Explanation:
Required Run rate = ( 314 - ( 5.4 x 30 ) )/ (20)
= ( 152) /(20) = 7.6
7. A man spends Rs. 1600 per month on an average for the first three months, Rs 1550 for next four months and Rs. 1800 per month for the last five months and saves Rs . 5200 a year. What is his average monthly income (in Rs.)?
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Correct Ans:2100
Explanation:
Total expenditure for the first 3 months = 3 Ã— 1600 = 4800
Total expenditure for 4 months = 4 Ã— 1550 = 6200
Total expenditure for 5 months = 5 Ã— 1800 = 9000
Total expenditure and saving (which is income for one year)
= 4800 + 6200 + 9000 + 5200 = Rs. 25200
So, Average monthly income = 25200/12 = Rs. 2100
8. The average of 18 numbers is zero. Of them, at the most how many may be greater than zero?
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Correct Ans:17
Explanation:
Average of 18 numbers = 0
Therefore, sum of all 18 numbers = 0
It is quite possible that 17 of these numbers may be positive and if their sum is "a" then 18th number is "(-a)".
So, all 17 numbers are greater than zero.
9. In the first 25 overs of a cricket game, the run rate was only 1.3. What should be the run rate in the remaining 25 overs to reach the target of 287 runs?
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Correct Ans:10.18
Explanation:
Required Run rate = ( 287 - ( 1.3 x 25 ) )/ (25)
= ( 254.5) /(25) = 10.18
10. Of three numbers, the third is twice the second and the second is 4 times the first. If their average is 78, the smallest of the three numbers is:
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Correct Ans:18
Explanation:
Let first number be x.
So,2nd number = 4x and
3rd number = 8x.
Given average = 78
So,x + 4x + 8x = 78 Ã— 3 = 234.
=> 13x = 234
=> x = 234/13
Hence, Smallest Number x=18.
11. The average of 16 numbers is zero. Of them, at the most how many may be greater than zero?
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Correct Ans:15
Explanation:
Average of 16 numbers is = 0
Therefore sum of all 16 numbers = 0
It is quite possible that 15 of these numbers may be positive and if their sum is "a" then 16th number is "(-a)".
12. In the first 10 overs of a cricket game, the run rate was only 6.2. What should be the run rate in the remaining 40 overs to reach the target of 414 runs?
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Correct Ans:8.8
Explanation:
Required Run rate = ( 414 - ( 6.2 x 10 ) )/ (40)
= ( 352) /(40) = 8.8
13. There were 45 students in a hostel, if the numbers of students increased by 7, the expenses of the mess were increased by Rs. 39 per day while the average expenditure per head diminished by Re.1. What is the original expenditure of the mess (in Rs)?
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Correct Ans:585
Explanation:
Let the original expenditure be Rs.x
Original average expenditure = X/45
New average expenditure = (x+39)/52
So (x/45) - ((x+39) / 52) = 1
=> (52x - 45x - 45 * 39) / (45 * 52) = 1
=> (7x - 1755) / 2340 = 1
=> 7x = 2340 + 1755
=> 7x = 4095
so x = 585
so, original expenditure is Rs 585
14. The average of 14 numbers is zero. Of them, at the most how many may be greater than zero ?
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Correct Ans:13
Explanation:
Average of 14 numbers is = 0
Therefore sum of all 14 numbers = 0
It is quite possible that 13 of these numbers may be positive and if their sum is "a" then 14th number is "(-a)"
15. In the first 10 overs of a cricket game, the run rate was only 5.6. What should be the run rate in the remaining 40 overs to reach the target of 254 runs?
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Correct Ans:4.95
Explanation:
Given
Target = 254 runs
First 10 overs, run rate = 5.6
Required Run rate
= ( 254 - ( 5.6 x 10 ) / (40)
= (198 ) / (40)
=4.95
16. The average weight of a class of 20 boys was calculated to be 58.4 kgs and it was later found that one weight was misread as 56 kg instead of 65 kg. What is the correct weight?
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Correct Ans:58.85
Explanation:
Actual total weight is (20 X 58.4 - 56 + 65) = 1177 Kgs
Actual average weight is 1177/20 = 58.85 kgs
17. The average of 12 numbers is zero. Of them, at the most how many may be greater than zero?
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Correct Ans:11
Explanation:
Average of 12 numbers is = 0
Therefore sum of all 12 numbers = 0
It is quite possible that 11 of these numbers may be positive and if their sum is "a" then 12th number is "(-a)"
18. In the first 25 overs of a cricket game, the run rate was only 2.2. What should be the run rate in the remaining 25 overs to reach the target of 225 runs ?
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Correct Ans:6.8
Explanation:
Required Run rate = ( 225 - ( 2.2 x 25 ) )/ (25)
= ( 170) /(25)
= 6.8
19. Average of 13 results is 65. If the average of first six results is 61 and average of last six results is 59. Then find the seventh result?
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Correct Ans:125
Explanation:
Given,Average of 13 results is 65.
Total result = Average * No. of results
=> Total result = 13 x 65 = 845
Given,average of first six results = 61
=> Total of first six = 61 * 6 = 366 and
Given,average of last six results is 59
=> Total for last six = 59 * 6 = 354
Then,
Seventh result = Total result – (Total of first six + Total for last six)
= 845 - ( 366 + 354 )
= 125
Therfore, Seventh result = 125
20. The average of 10 numbers is zero. Of them, at the most how many may be greater than zero?
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Correct Ans:9
Explanation:
Average of 10 numbers is = 0
Therefore sum of all 10 numbers = 0
It is quite possible that 9 of these numbers may be positive and if their sum is "a" then 10th number is "(-a)".
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