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Yourself:While finding the average of ‘9’ consecutive numbers starting from X; a student interchanged the digits of second number by mistake and got the average which is 8 more than the actual. What is X?
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Yourself:While finding the average of ‘9’ consecutive numbers starting...
Understanding the Problem:
The student has mistakenly interchanged the digits of the second number while finding the average of 9 consecutive numbers starting from X. This error resulted in an average that is 8 more than the actual average.
Solving the Problem:
Let's assume the 9 consecutive numbers starting from X are X, X+1, X+2, X+3, X+4, X+5, X+6, X+7, and X+8.
The actual average of these numbers would be (X + X+1 + X+2 + X+3 + X+4 + X+5 + X+6 + X+7 + X+8) / 9 = X + 4.
When the student interchanged the digits of the second number, let's say the new number is Y. So, the new series becomes X, Y, X+2, X+3, X+4, X+5, X+6, X+7, and X+8.
The new average is (X + Y + X+2 + X+3 + X+4 + X+5 + X+6 + X+7 + X+8) / 9 = X + 4 + 8 = X + 12.
Finding the Value of X:
Since the new average is 8 more than the actual average, we can equate the two expressions:
X + 12 = X + 4 + 8
X + 12 = X + 12
X = 0
Therefore, the value of X is 0. The 9 consecutive numbers starting from 0 would be 0, 1, 2, 3, 4, 5, 6, 7, and 8.
By following the steps above and understanding the problem thoroughly, we can determine the correct value of X, which is essential in solving this type of mathematical puzzle.
The student has mistakenly interchanged the digits of the second number while finding the average of 9 consecutive numbers starting from X. This error resulted in an average that is 8 more than the actual average.
Solving the Problem:
Let's assume the 9 consecutive numbers starting from X are X, X+1, X+2, X+3, X+4, X+5, X+6, X+7, and X+8.
The actual average of these numbers would be (X + X+1 + X+2 + X+3 + X+4 + X+5 + X+6 + X+7 + X+8) / 9 = X + 4.
When the student interchanged the digits of the second number, let's say the new number is Y. So, the new series becomes X, Y, X+2, X+3, X+4, X+5, X+6, X+7, and X+8.
The new average is (X + Y + X+2 + X+3 + X+4 + X+5 + X+6 + X+7 + X+8) / 9 = X + 4 + 8 = X + 12.
Finding the Value of X:
Since the new average is 8 more than the actual average, we can equate the two expressions:
X + 12 = X + 4 + 8
X + 12 = X + 12
X = 0
Therefore, the value of X is 0. The 9 consecutive numbers starting from 0 would be 0, 1, 2, 3, 4, 5, 6, 7, and 8.
By following the steps above and understanding the problem thoroughly, we can determine the correct value of X, which is essential in solving this type of mathematical puzzle.
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Yourself:While finding the average of ‘9’ consecutive numbers starting from X; a student interchanged the digits of second number by mistake and got the average which is 8 more than the actual. What is X?
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Yourself:While finding the average of ‘9’ consecutive numbers starting from X; a student interchanged the digits of second number by mistake and got the average which is 8 more than the actual. What is X? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Yourself:While finding the average of ‘9’ consecutive numbers starting from X; a student interchanged the digits of second number by mistake and got the average which is 8 more than the actual. What is X? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Yourself:While finding the average of ‘9’ consecutive numbers starting from X; a student interchanged the digits of second number by mistake and got the average which is 8 more than the actual. What is X?.
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