Q. 53.8( 38 Votes )

A two-digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits. Find the number.

Answer :

Let the unit digit be 'x'


Let the digit at ten's place be 'y'


The original number will be 10y + x


Given, number is 3 more than 4 times the sum of its digits


10y + x = 4(x + y) + 3


10y + x = 4x + 4y + 3


6y - 3x = 3


2y - x = 1


x = 2y - 1 eq.[1]


Also,


If the digits are interchanged,


Reversed number will be = 10x + y


As, reversed number exceeds the original number by 18,


(10x + y) - (10y + x) = 18


10x + y - 10y - x = 18


9x - 9y = 18


x - y = 2


2y - 1 - y = 2 eq.[using 1]


y = 3


Using this in eq.[1]


x = 2(3) - 1 = 5


Hence the original number is 10y + x = 10(3) + 5 = 30 + 5 = 35.


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