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A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18?
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A student finds the average of 10 positive integers. Each integer cont...
Problem: Find the difference between the two digits a and b when the student finds the average of 10 positive integers, each containing two digits, and interchanges the digits of one number, causing the average to become 1.8 less than the previous one.
Solution:
Let the original sum of the 10 integers be S and the original average be A. Then we have:
S = 10A
Let the number whose digits are interchanged be xy, and let the corrected average be B. Then we have:
S + y - x = 10B
And we also know that:
B = A - 1.8
Substituting the value of B in terms of A in the second equation, we get:
S + y - x = 10(A - 1.8)
S + y - x = 10A - 18
Substituting the value of S in terms of A from the first equation, we get:
10A + y - x = 10A - 18
y - x = -1.8
Since x and y are digits, they must be integers between 0 and 9. Therefore, the only possible values for x and y that satisfy the equation are:
x = 9 and y = 8
Therefore, the difference between the two digits a and b is:
a - b = x - y = 9 - 8 = 1
Answer: 1
Solution:
Let the original sum of the 10 integers be S and the original average be A. Then we have:
S = 10A
Let the number whose digits are interchanged be xy, and let the corrected average be B. Then we have:
S + y - x = 10B
And we also know that:
B = A - 1.8
Substituting the value of B in terms of A in the second equation, we get:
S + y - x = 10(A - 1.8)
S + y - x = 10A - 18
Substituting the value of S in terms of A from the first equation, we get:
10A + y - x = 10A - 18
y - x = -1.8
Since x and y are digits, they must be integers between 0 and 9. Therefore, the only possible values for x and y that satisfy the equation are:
x = 9 and y = 8
Therefore, the difference between the two digits a and b is:
a - b = x - y = 9 - 8 = 1
Answer: 1
Community Answer
A student finds the average of 10 positive integers. Each integer cont...
Average = sum of all numbers/No. Of numbers
The number is 'ab' i. e. 10a+b
Numbr formed by interchanging digits will be 'ba' i. E. 10b+a
Let sum of first 9 numbers be x
Difference between averages:
1.8 = (x+10a+b)/10 - (x+10b+a1)/10
18= x+10a+b - x-10a-b
18=9a-9b
Therefore,
(a-b) =2
The number is 'ab' i. e. 10a+b
Numbr formed by interchanging digits will be 'ba' i. E. 10b+a
Let sum of first 9 numbers be x
Difference between averages:
1.8 = (x+10a+b)/10 - (x+10b+a1)/10
18= x+10a+b - x-10a-b
18=9a-9b
Therefore,
(a-b) =2
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A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18?
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A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18?.
A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A student finds the average of 10 positive integers. Each integer contains two digits. By mistake, the student interchanges the digits of one number say ba for ab. Due to this, the average becomes 1.8 less than the previous one. What is the difference between the two digits a and b? 1. 8 2. 6 3. 2 4. 4 5. 18?.
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