In a two digit number the …
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Preeti Dabral 1 year, 4 months ago
Let the digit in the unit's place be x and the digit in the ten's place be y.
Then, Number =10y + x
According to the given condition, we have
The ten's digit is three times the unit's digit.
y = 3x ..............(i)
Number obtained by reversing the digits =10x + y
If the number is decreased by 54, the digits are reversed.
{tex}\therefore{/tex} Number - 54 =Number obtained by reversing the digits
⇒ 10y + x -54 =10x + y
⇒ x - 10x + 10y - y = 54
⇒ - 9x + 9y = 54
⇒ 9x - 9y =-54
⇒ x - y =-6 ............(ii)
Putting y = 3x in equation (ii), we get
⇒ x - y = 6
⇒ x - 3x = -6
⇒ - 2x = -6
⇒ x = 3
Putting x = 3 in y = 3x, we get y =9
The number = 10y + x = 10{tex}\times{/tex} 9 + 3 = 90 + 3 = 93
Hence the given two digit number is 93.
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