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Sonam calculates average of 10 positive 2 digit integers. By mistake she interchanges the digits of one number while calculating the average. Because of which, the average becomes 2.7 less than the correct answer. What is the difference between the two digits of the number which was reversed while calculating the average?
- a)3
- b)7
- c)5
- d)10
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Sonam calculates average of 10 positive 2 digit integers. By mistake s...
Solution:
Let the original 2-digit number be 'ab' where a and b are digits.
The correct average of 10 positive 2-digit integers is:
= (a1 + a2 + a3 + ... + a10)/10
where a1, a2, a3,...,a10 are 10 positive 2-digit integers.
After interchanging the digits of one number, the new number becomes 'ba', which increases the sum of all 10 numbers by (b-a) and the average of 10 numbers by (b-a)/10.
So, the new average becomes:
= (a1 + a2 + a3 + ... + a10 + b - a)/10
According to the question, the new average is 2.7 less than the correct average. So, we can write:
(a1 + a2 + a3 + ... + a10 + b - a)/10 = (a1 + a2 + a3 + ... + a10)/10 - 2.7
Simplifying this equation, we get:
b - a = 27/10
Multiplying both sides by 10, we get:
10b - 10a = 27
Dividing both sides by 2, we get:
5b - 5a = 27/2
Since a and b are digits, the only possible values for (5b - 5a) are 5, 10, 15, 20, 25, and 30.
We can see that only 5 satisfies the equation, which means:
5b - 5a = 27/2
5b - 5a = 13.5
b - a = 2.7
So, the difference between the two digits of the number which was reversed while calculating the average is 3 (since b - a = 2.7 ≈ 3).
Therefore, the correct answer is option 'A'.
Let the original 2-digit number be 'ab' where a and b are digits.
The correct average of 10 positive 2-digit integers is:
= (a1 + a2 + a3 + ... + a10)/10
where a1, a2, a3,...,a10 are 10 positive 2-digit integers.
After interchanging the digits of one number, the new number becomes 'ba', which increases the sum of all 10 numbers by (b-a) and the average of 10 numbers by (b-a)/10.
So, the new average becomes:
= (a1 + a2 + a3 + ... + a10 + b - a)/10
According to the question, the new average is 2.7 less than the correct average. So, we can write:
(a1 + a2 + a3 + ... + a10 + b - a)/10 = (a1 + a2 + a3 + ... + a10)/10 - 2.7
Simplifying this equation, we get:
b - a = 27/10
Multiplying both sides by 10, we get:
10b - 10a = 27
Dividing both sides by 2, we get:
5b - 5a = 27/2
Since a and b are digits, the only possible values for (5b - 5a) are 5, 10, 15, 20, 25, and 30.
We can see that only 5 satisfies the equation, which means:
5b - 5a = 27/2
5b - 5a = 13.5
b - a = 2.7
So, the difference between the two digits of the number which was reversed while calculating the average is 3 (since b - a = 2.7 ≈ 3).
Therefore, the correct answer is option 'A'.
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Community Answer
Sonam calculates average of 10 positive 2 digit integers. By mistake s...
Let the original number be (10b+a)
Because of interchange, the mistaken number is (10a+b)
Given that, 10b+a = 10a+b +(2.7*10) => 9b-9a = 27 => b-a = 3
So, the correct answer is A.
So, the correct answer is A.
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Sonam calculates average of 10 positive 2 digit integers. By mistake she interchanges the digits of one number while calculating the average. Because of which, the average becomes 2.7 less than the correct answer. What is the difference between the two digits of the number which was reversed while calculating the average?a)3b)7c)5d)10Correct answer is option 'A'. Can you explain this answer?
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