the digit in the units place of a two digit number is obtained by subtracting 1 from the square of the digit in the tens place. the digits gets interchanged when the digit in the tens place is multiplied by 16.what is the original number?
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Answer:
23
Step-by-step explanation:
Let x and y be the digits. Number = 10x+y
y = x² - 1
16x = 10y+x
15x = 10y
=> y = 3x/2
substitute the above value of y in equation y = x² - 1
3x/2 = x² - 1
3x = 2x² - 2
2x² - 3x - 2 = 0
2x² - 4x + x -2 = 0
2x(x-2) + 1(x-2) = 0
(2x + 1 )(x-2) =
=> x = 2
=> y = 3
Hence original number = 10*2 + 3 = 23.
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