Question

The sum of the digits of a 2-digit number is 6. The original number is 18 more than the number obtained by reversing the digits. Find the number​

Answer 1

Answer:

42

Step-by-step explanation:

4+2=6

On reversing we get 24, and 42-24 is 18

Answer 2

$\bigstar \mid$ Given :

• Sum of digital number having their sum as 6.
• The difference between the original no. and the no. obtained by reversing the digital is 18.

$\bigstar \mid$ To find :

The number.

$\bigstar \mid$ Solution :

Let's assume that the no. formed by the two digits are :

x (ones place) and y (tens place)

Their sum :

$\longmapsto { {\bf{x + y = 6 }}} \: \: \: \: \gray{ \sf{(given)}}$

The no. formed :

$\longmapsto \bf { 10x + y }$

By reversing the digits :

or,

The New number :

$\longmapsto \bf { 10y + x }$

$\begin{gathered}\underline{\boldsymbol{☯ According\: to \:the\: question :}}\\\end{gathered}$

$\bf \implies (10x + y) - (10y + x) = 18$

${\gray {\sf{(opening \: brackets)}}}$

$\bf \implies 10x + y - 10y - x = 18$

$\bf \implies 9x - 9y = 18$

${ \gray{ \sf{(taking \: common)}}}$

$\bf \implies 9(x - y) = 18$

$\bf \implies \: x - y = { \cancel{\frac{18}{9}}}$

$\bf \implies x - y = 2$

Now,

We have :

$\bf \longmapsto \: x + y = 6 ......(i)$

$\bf \longmapsto \: x - y = 2 .........(ii)$

Subtraction of both the equation as follows :

$\bf \cancel x + y = 6 \\ {\bf{ \underline{ - \cancel x + y = 2}}} \\ \bf \implies 2y = 4 \\ \bf \implies \: y = { \cancel{\frac{4}{2} }} \\ \bf \therefore \: y = 2$

Substituting the value of y in the equation (i) as follows :

$\tt \implies \: x + y = 6$

$\tt \implies \: x + 2 = 6$

$\tt \implies \: x = 6 - 2$

$\bf \implies \: x = 4 \: ans.$

Forming the number as follows :

↪ ️$\bf \: 10x + y$

↪ ️$\bf \: (10 \times 4) + 2$

↪️ $\bf \: 42 \: or \: 24 \: ans.$

${\underbrace{ \boxed{ \textbf{ \textsf{Required \: answer }}}}} \\ {\underline{ \boxed{ \textbf{ \textsf{The \: number \: can \: be \: 42 \: or, \: 24}}}}}$