The ten’s digit of a two digit number is twice the digit in the unit’s place. If the ten’s digit is made half and if units digit is doubled then the new number obtained is less than the original number by 27. Find the number.
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Let the units digit be y and tens digit be x. Then, the number is
10x + y, and x = 2y.
If x is halved and y is doubled, then, the new number is
10x/2+2y = 10x+y-27.
5x+2y = 10x+y-27
5x-y=27
Substituting the value of x = 2y in the above equation, we get
10y-y = 27
or 9y=27. Thus, y = 3.
And x = 2*3 = 6.
Therefore the number is 63.
10x + y, and x = 2y.
If x is halved and y is doubled, then, the new number is
10x/2+2y = 10x+y-27.
5x+2y = 10x+y-27
5x-y=27
Substituting the value of x = 2y in the above equation, we get
10y-y = 27
or 9y=27. Thus, y = 3.
And x = 2*3 = 6.
Therefore the number is 63.
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