Question

The number obtained by interchanging the two digits of a two-digit number is less than the original number by 18. the sum of the two digits of the number is 16. what is the original number?

Answer 1

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Answer 2

Answer:

The original number is termed to be 97.

Solution:

Let the original no. be $=10y+x$

And the reversed no. will be $=10x+y$

According to the sum,  

$\begin{array} { c } { ( 10 y + x ) - ( 10 x + y ) = 18 } \\\\ { 10 y + x - 10 x - y = 18 } \\\\ { 9 y - 9 x = 18 } \\\\ { 9 ( y - x ) = 18 } \\\\ { ( y - x ) = \frac { 18 } { 9 } = 2 } \\\\ { x - y = - 2 \quad \ldots ( i ) } \end{array}$

And,  

$\mathrm { x } + \mathrm { y } = 16 \quad \ldots \text { (ii) }$

(i) + (ii),

$\begin{array} { c } { 2 x = 14 } \\\\ { x = \frac { 14 } { 2 } = 7 } \end{array}$

Putting x =7 in (ii), we get,

$\begin{array} { c } { 7 + y = 16 } \\\\ { y = 16 - 7 = 9 } \end{array}$

Hence, the original number is  

$( 10 y ) + x = ( 10 \times 9 ) + 7 = 97$

Therefore, the original number will be 97.