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# Average Questions | UPSC CSAT

Average Questions

What is Average of Numbers?

To calculate the average of a set of numbers, you need to add up all the numbers and then divide the sum by the total count of numbers.

Average = (Sum of all numbers) / (Total count of numbers)

For example, let’s say you have the numbers 5, 10, 15, and 20. To find their average:

Sum of all numbers = 5 + 10 + 15 + 20 = 50

Total count of numbers = 4

Average = 50 / 4 = 12.5

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Question 1: The average of five numbers is 12. If one number is excluded, the average becomes 10. What is the excluded number?
(a) 12
(b) 20
(c) 14
(d) 8

Ans: (b)

Explanation: Let’s assume the sum of the five numbers is x.

Therefore, the average of the five numbers is x/5 = 12.
This implies that x = 12 * 5 = 60.

If one number is excluded, then the sum of the remaining four numbers is 60 – excluded number.
The new average is given as (60 – excluded number)/4 = 10.
Simplifying the equation, we have 60 – excluded number = 40.
Therefore, the excluded number is 60 – 40 = 20.

Question 2: The average of four consecutive even numbers is 24. What is the largest number?
(a) 27
(b) 28
(c) 30
(d) 32

Ans: (a)

Explanation: Let’s assume the first even number is x. The next three consecutive even numbers will be x + 2, x + 4, and x + 6.
The sum of these four numbers is x + (x + 2) + (x + 4) + (x + 6) = 4x + 12.
According to the question, the average is 24, so we have (4x + 12)/4 = 24.
Simplifying the equation, we get 4x + 12 = 96.
Solving for x, we find x = 21.
The largest number is x + 6 = 21 + 6 = 27.

Question 3: The average of seven numbers is 18. If one number, 12, is added, what will be the new average?
(a) 18.75
(b) 20
(c) 19.25
(d) 17.25

Ans: (d)

Explanation:
The sum of the seven numbers is 7 * 18 = 126.
If one number, 12, is added, the new sum becomes 126 + 12 = 138.
The new average is the new sum divided by the new count, which is (138)/(7 + 1) = 138/8 = 17.25.

Question 4: The average of five numbers is 16. If each number is multiplied by 3, what will be the new average?
(a) 16
(b) 32
(c) 48
(d) 8

Ans: (c)

Explanation: When each number is multiplied by 3, the new sum becomes 3 times the original sum.
Therefore, the new sum is 3 * 5 * 16 = 240.
The new average is the new sum divided by the original count, which is 240/5 = 48.

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Question 5: The average of three numbers is 15. If two of the numbers are 12 and 18, what is the third number?
(a) 8
(b) 12
(c) 15
(d) 22

Ans: (c)

Explanation: The sum of the three numbers is 3 * 15 = 45.
If two of the numbers are 12 and 18, the sum of these two numbers is 30. Hence the required number is 15.

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