If two digit number it's tens digit number three times is unit digit. If the interchange number find new number. Difference between original number and new number is 54. Find the original number.
Step to step explaination.
Step to step explaination.
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Answer:
Step-to-step explanation:
Let's say the original two-digit number is represented as "10x + y", where x is the tens digit and y is the units digit.
According to the problem statement, we have:
x = 3y ... (1)
This means that the tens digit is three times the units digit.
If we interchange the digits, the new number becomes "10y + x". The difference between the original number and the new number is given as 54, so we have:
(10x + y) - (10y + x) = 54
Simplifying the above equation, we get:
9x - 9y = 54
Dividing both sides by 9, we get:
x - y = 6 ... (2)
We can now use equations (1) and (2) to solve for x and y. Substituting x = 3y from equation (1) into equation (2), we get:
3y - y = 6
Solving for y, we get:
y = 2
Substituting y = 2 into equation (1), we get:
x = 3y = 3(2) = 6
Therefore, the original two-digit number is 62.
To check, if we interchange the digits to get 26, the difference between the original number (62) and the new number (26) is indeed 54.
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