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Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to?
Verified Answer
Anmol was asked to calculate earth Matic mean of 10 positive integers ...
Let the actual average be n. So, the new average is n + 1.8
Actual total = 10n
New total = 10n + 18
Let the number which was miswritten = ab(a is the tenth's digit and b is the units digit) = 10a + b
and reversed number ba = 10b + a
So, 10b + a - (10a + b) = 18
=> 9(b - a) = 18
=> b - a = 2
Actual total = 10n
New total = 10n + 18
Let the number which was miswritten = ab(a is the tenth's digit and b is the units digit) = 10a + b
and reversed number ba = 10b + a
So, 10b + a - (10a + b) = 18
=> 9(b - a) = 18
=> b - a = 2
This question is part of UPSC exam. View all CAT courses
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Anmol was asked to calculate earth Matic mean of 10 positive integers ...
Calculation Mistake in Arithmetic Mean
Anmol made a mistake by interchanging the two digits a and b in one of the 10 integers while calculating the arithmetic mean.
Given Information
Let's assume the 10 integers are x1, x2, x3, ..., x10. The correct arithmetic mean should have been M.
Anmol's incorrect arithmetic mean calculation (after interchanging digits a and b) is M + 1.8.
Finding the Correct Arithmetic Mean
To find the correct arithmetic mean, we need to first identify the difference between the incorrect and correct arithmetic means.
The difference is 1.8, which means that the sum of the 10 integers was increased by 18 (1.8 * 10).
Finding the Digits a and b
When the digits a and b are interchanged in one of the integers, the difference in the sum of the digits is b - a.
Since the sum of the 10 integers increased by 18, this increase must be due to the difference in the sum of the interchanged digits in one of the integers.
Therefore, b - a = 18.
Conclusion
The difference between the interchanged digits a and b in one of the 10 integers is 18.
Anmol made a mistake by interchanging the two digits a and b in one of the 10 integers while calculating the arithmetic mean.
Given Information
Let's assume the 10 integers are x1, x2, x3, ..., x10. The correct arithmetic mean should have been M.
Anmol's incorrect arithmetic mean calculation (after interchanging digits a and b) is M + 1.8.
Finding the Correct Arithmetic Mean
To find the correct arithmetic mean, we need to first identify the difference between the incorrect and correct arithmetic means.
The difference is 1.8, which means that the sum of the 10 integers was increased by 18 (1.8 * 10).
Finding the Digits a and b
When the digits a and b are interchanged in one of the integers, the difference in the sum of the digits is b - a.
Since the sum of the 10 integers increased by 18, this increase must be due to the difference in the sum of the interchanged digits in one of the integers.
Therefore, b - a = 18.
Conclusion
The difference between the interchanged digits a and b in one of the 10 integers is 18.
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Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to?
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Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to?.
Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Anmol was asked to calculate earth Matic mean of 10 positive integers each of insured to did it by mistake interchange the two digit say a and b In one of these 10 integers as a result his answer for the earth Matic mean was 1.8 more than wanted should have been then b-a is equal to?.
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