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01. If from a group of 5 people, an old member is replaced by a new one, the average age is same as it was 3 years ago. What is the difference between the ages of the old member and the new one?
A. 12 B. 15
C. 11 D. 18

Answer and Explanation

Answer: 15

Explanation:
The present average age is (x + 3) when the old member is present and it equals to x when an old member is replaced by a new one.
The difference in the ages of the old member and the new one is equal to the difference in the total age before and after the replacement = 15 years.

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02. The average of 20 numbers is zero. Of them, at the most, how many may be greater than zero?
A. 0 B. 1
C. 10 D. 19

Answer and Explanation

Answer: 19

Explanation:
Average of 20 numbers = 0.
Sum of 20 numbers (0 x 20) = 0.
It is quite possible that 19 of these numbers may be positive and if their sum is a then 20th number is (-a).

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03. A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
A. Rs. 7.98 B. Rs. 8
C. Rs. 9 D. Rs. 8.50

Answer and Explanation

Answer: Rs. 7.98

Explanation:

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04. The batting average of a particular batsman is 60 runs in 46 innings. If the difference in his highest and lowest score is 150 runs and his average excluding these two innings is 58 runs, find his highest score.
A. 179 B. 208
C. 210 D. None of these

Answer and Explanation

Answer: 179

Explanation:
Total runs scored by the batsman = 60*46 = 2760 runs
Now excluding the two innings the runs scored = 58*44 = 2552 runs
Hence the runs scored in the two innings = 2760 – 2552 = 208 runs.
Let the highest score be x, hence the lowest score = x – 150
x + (x - 150) = 208
2x = 358
x = 179 runs

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05. The average of 8 results is 20. The average of first two results is 15 ½. The average of next three results is 21 1/3. The sixth result is 4 less than the seventh and 7 less than the 8th. Find the last result.
A. 23 B. 22
C. 25 D. 21

Answer and Explanation

Answer: 25

Explanation:
Sum of 8 results = 8(20) =160
Sum of first two results = 2(15.5) = 31
Sum of next three results = 3(21 1/3) = 64
The sixth result be x, Seventh result = x+4 Eighth result = x+7
31 + 64 + x + x + 4 + x + 7 = 160
X = 18, so last result = 18+7 =25

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06. The average marks secured by 36 students is determined as 52. But it is later discovered that the mark 64 was wrongly entered as 46. What is correct average of marks of the 36 students?
A. 52.5 B. 52
C. 53 D. 51.5

Answer and Explanation

Answer: 52.5

Explanation:
Total marks secured by 36 students = 52 × 36 = 1872
Total marks secured by 36 students(Corrected) =1872-46+64 = 1890
∴Correct Average = 1890 / 36 = 52.5
Alternatively, Increase in the total marks when the error is corrected = 64-46 = 18.
The average of 32 students will increase by 18/36 = 0.5.
Hence the corrected average = 52 + 0.5 = 52.5

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07. In a party there were 8 men, when 2 of these men aged 20 and 24 left the party and 2 women entered the party, the average age of the entire group of 8 increased by 2. What was the average age of the two new women entered the party?
A. 35 B. 32
C. 30 D. 33

Answer and Explanation

Answer: 30

Explanation:
Average age of X1 = ∑Xmen / 8 (1)
= ∑Xmen = 8X1
Let ages of two women be A, B
∑X new = ∑X men – (20 +24) + (A + B)
X1 + 2 = (= ∑X men – 44 + (A + B)) / 8
Equations (1) and (2) gives:
44/8 – (A + B)/8 = -2
44 – (A +B) = -16
A + B = 60
Average age of women = 60/2 = 30 years

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08. 30 horses were purchased for Rs. 12000. Out of the 30 horses, the average cost of the 12 horses is Rs. 250. Find the average cost of the remaining horses.
A. Rs. 600 B. Rs. 500
C. Rs. 550 D. Rs. 650

Answer and Explanation

Answer: Rs. 500

Explanation:
The total cost of 30 horses = Rs. 12000.
The cost of the 12 horses = Average cost of 12 horses × 12 =250 ×12= 3000.
The cost of the remaining 18 horses, = 9000 / (30 – 12) = 9000 / 18 = Rs. 500

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09. The average salary per head on all the workers and officers in a workshop is Rs 95. The average salary in 15 officers is Rs 525 and the average salary of the workers is Rs 85. Find the number of workers in the workshop.
A. 600 B. 645
C. 690 D. 654

Answer and Explanation

Answer: 645

Explanation:
Let the number of workers be x
85x + 525(15) = 95(x + 15) =>x = 645

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10. A batsman is out for 23 runs, which raises his average for the season from 15 to 16. How many runs would he have to score in that innings (in which he scored 23) to bring his average up to 18?
A. 33 B. 37
C. 39 D. 42

Answer and Explanation

Answer: 39

Explanation:
Had the batsman scored 15 runs in the last inning, his average would have been constant at 15. He scores 8 runs more than 15, which raises his average by 1.
∴ The last must have been his 8 / 1 = 8th innings.
To raise his average by 3, he required to score 8 × 3 = 24 runs more than his previous average in the 8th innings => he need to score 39

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