Question

the sum of the digits of a two digits number and the number obtained by reversing the order of digits iS 121 if yhe digits differ by 4 find the number
​

Answer 1

QUESTION

The sum of a two digit number and the number obtained by reversing the order of its digits is 121, and the two digits differ by 3.  Find the number.

                                                         

SOLUTION

Let the ten's digit be x and the one's digit be y.

Given

$10x+y+10y+x=121\\\implies 11x+11y=121\\\implies 11(x+y)=121\\\implies x + y = 11 -- (1)$

Assuming, x > y

$x- y= 3 --- (2)$

Solving (1) and (2), we get,

$x+y=11\\\underline{x-y=3}\\\underline{\underline{2x = 14}}\\\implies x = 7\\\implies y = 4$

If y>x

$\implies y = 7\\\implies x = 4$

$\boxed{\boxed{\bold{Therefore, \ the \ number \ is \ 47 \ or \ 74.}}}}}$