Question

The sum of digits of a two digit number is 7.The number obtained,on reversing the order of digits is greater than original number by 9. Find the number.
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Answer 1

Step-by-step explanation:

let the no.s be x and y

then x+y= 7 (according to question )

ATQ, 10x+y+9=10y+x

=9y-9x=9

=y-x=1

then x+y+y-x= 7+1

2y=8

y=4

x=3

NO.= 34

Answer 2

$\bf{\Huge{\boxed{\tt{\red{ANSWER\::}}}}}$

$\bf{\Large{\underline{\sf{Given\::}}}}$

The sum of digit of a two digit number is 7. The number obtained, on reversing the order of digits is greater than original number by 9.

$\bf{\Large{\underline{\sf{To\:find\::}}}}$

The number.

$\bf{\Large{\underline{\rm{\green{Explanation\::}}}}}$

• Let the ten's digit be M.
• Let the unit's digit be R.

A/q

$\longmapsto\tt{M\:+\:R\:=\:7......................(1)}$

When the digits are reversed, the number is 9 more than original number.

$\rm{The\:original\:number\:=\:10R+M}$

$\rm{The\:reversed\:Number\:=\:10M+R}$

So,

$\mapsto\tt{10M +R\:=\:10R+M+9}$

$\mapsto\tt{10M-M+R-10R=9}$

$\mapsto\tt{9M\:-\:9R\:=\:9}$

$\mapsto\tt{9(M-R)=9}$

$\mapsto\tt{M\:-\:R\:=\:\cancel{\frac{9}{9} }}$

$\mapsto\tt{M\:-\:R\:=\:1...........................(2)}$

$\bf{\Large{\boxed{\rm{Using\:Substitution\:Method\::}}}}}}$

From equation (1), we get;

$\longmapsto\sf{M+R\:=\:7}$

$\longmapsto\sf{M\:=7-R............................(3)}$

Putting the value of M in equation (2), we get;

$\longmapsto\sf{7\:-\:R\:-\:R\:=\:1}$

$\longmapsto\sf{7\:-2R\:=\:1}$

$\longmapsto\sf{-2R\:=\:1-7}$

$\longmapsto\sf{-2R\:=\:-6}$

$\longmapsto\sf{R\:=\:\cancel{\frac{-6}{-2} }}$

$\longmapsto\sf{\red{R\:=\:3}}$

Putting the value of R in equation (3), we get;

$\longmapsto\sf{M\:=\:7-3}$

$\longmapsto\sf{\red{M\:=\:4}}$

Thus,

$\leadsto\rm{The\:original\:number\:is\:10R+M}$

$\leadsto\rm{The\:original\:number\:is\:10(3)+4}$

$\leadsto\rm{\red{The\:original\:number\:is\:30+4\:=\:34.}}$