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The average of twelve 2 digit numbers is decreased by 3 when the digits of one of the 2 digit numbers is interchanged. Find the difference between the digits of that number.
- a)4
- b)5
- c)2
- d)6
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The average of twelve 2 digit numbers is decreased by 3 when the digit...
Given Information:
The average of twelve 2-digit numbers is decreased by 3 when the digits of one of the 2-digit numbers are interchanged.
Solution:
To solve this problem, let's consider the sum of the twelve 2-digit numbers as S and the average as A.
Step 1: Initial Average Calculation
Initially, the average of the twelve 2-digit numbers is:
A = S/12
Step 2: Average Decreased by 3
When the digits of one of the 2-digit numbers are interchanged, the new average becomes:
A - 3 = S/12
Step 3: Finding the Interchanged Number
Let's assume the original number is 10x + y, where x and y are the digits.
The new number will be 10y + x.
The difference between the original number and the new number is:
(10x + y) - (10y + x) = 9(x - y)
Step 4: Difference Calculation
As the average decreases by 3, we have:
9(x - y) = 3
x - y = 3/9
x - y = 1/3
Therefore, the difference between the digits of the interchanged number is 3.
Conclusion:
The correct option is a) 4, as the difference between the digits of the interchanged number is 3.
The average of twelve 2-digit numbers is decreased by 3 when the digits of one of the 2-digit numbers are interchanged.
Solution:
To solve this problem, let's consider the sum of the twelve 2-digit numbers as S and the average as A.
Step 1: Initial Average Calculation
Initially, the average of the twelve 2-digit numbers is:
A = S/12
Step 2: Average Decreased by 3
When the digits of one of the 2-digit numbers are interchanged, the new average becomes:
A - 3 = S/12
Step 3: Finding the Interchanged Number
Let's assume the original number is 10x + y, where x and y are the digits.
The new number will be 10y + x.
The difference between the original number and the new number is:
(10x + y) - (10y + x) = 9(x - y)
Step 4: Difference Calculation
As the average decreases by 3, we have:
9(x - y) = 3
x - y = 3/9
x - y = 1/3
Therefore, the difference between the digits of the interchanged number is 3.
Conclusion:
The correct option is a) 4, as the difference between the digits of the interchanged number is 3.
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Community Answer
The average of twelve 2 digit numbers is decreased by 3 when the digit...
Given:
The average of twelve 2 digit numbers is decreased by 3 when the digits of one of the 2 digit numbers is interchanged.
Formula used:
Average = sum of observations/ Number of observations
Calculation:
Let the number whose digits are being interchanged is 10x + y
After interchanging the digits, the number becomes 10y + x
At first average = (sum of 11 numbers + 10x + y)/12
After interchanging the digits, average = (sum of 11 numbers + 10y + x)/12
So, (sum of 11 numbers + 10y + x)/12 = (sum of 11 numbers + 10x + y)/12 - 3
⇒ (sum of 11 numbers + 10y + x) = (sum of 11 numbers + 10x + y) - 36
⇒ 10y + x = 10x + y - 36
⇒ 9x - 9y = 36
⇒ x - y = 36/9
⇒ x - y = 4
∴ difference between two digits is 4.
The average of twelve 2 digit numbers is decreased by 3 when the digits of one of the 2 digit numbers is interchanged.
Formula used:
Average = sum of observations/ Number of observations
Calculation:
Let the number whose digits are being interchanged is 10x + y
After interchanging the digits, the number becomes 10y + x
At first average = (sum of 11 numbers + 10x + y)/12
After interchanging the digits, average = (sum of 11 numbers + 10y + x)/12
So, (sum of 11 numbers + 10y + x)/12 = (sum of 11 numbers + 10x + y)/12 - 3
⇒ (sum of 11 numbers + 10y + x) = (sum of 11 numbers + 10x + y) - 36
⇒ 10y + x = 10x + y - 36
⇒ 9x - 9y = 36
⇒ x - y = 36/9
⇒ x - y = 4
∴ difference between two digits is 4.
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The average of twelve 2 digit numbers is decreased by 3 when the digits of one of the 2 digit numbers is interchanged. Find the difference between the digits of that number.a)4b)5c)2d)6Correct answer is option 'A'. Can you explain this answer?
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