Question

a two digit number is 3 more than 4 times the sum of its digit if 18 is added to the number its digits are reversed find the number​

Answer 1

Answer: the number is 35

Step-by-step explanation:

Let 10x+ y represent the number.

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

6x-3y = 3

2x-y = 1......equation(i)

10x+y+18 = 10y+x

9x-9y= -18...equation (ii)

Solve the two equations simultaneously..

x= 3 and y= 5

The number is 10x+y = 10(3)+5 = 35

Answer 2

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

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

A two digit number is 3 more than 4 times the sum of its digit if 18 is added to the number its digit are reversed.

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

The number.

$\bf{\Large{\underline{\tt{\red{Explanation\::}}}}}$

Let the original number be 10M + R.

$\bf{We\:have}\begin{cases}\sf{The\:unit's\:place\:of\:number\:be\:\:R.}\\ \sf{The\:ten's\:place\:of\:number\:be\:\:M.}\end{cases}}$

A/q

$\implies\sf{10M+R\:=\:4(R+M)+3}$

$\implies\sf{10M+R\:=\:4R+4M+3}$

$\implies\sf{10M-4M+R-4R\:=\:3}$

$\implies\sf{6M-3R\:=\:3}$

$\implies\sf{3(2M-R)=3}$

$\implies\sf{2M-R\:=\:\cancel{\frac{3}{3}} }$

$\implies\sf{2M-R\:=\:1}$

$\implies\sf{2M\:=\:1+R}$

$\implies\sf{M\:=\:\dfrac{R+1}{2}.......................(1)}$

&

Reversed Number be 10R + M,

$\implies\sf{10M+R+18=10R+M}$

$\implies\sf{10M-M+R-10R\:=\:-18}$

$\implies\sf{9M-9R\:=\:-18}$

$\implies\sf{9(M-R)=-18}$

$\implies\sf{M-R\:=\:\cancel{-\frac{18}{9} }}$

$\implies\sf{M-R\:=\:-2}$

Putting the equation (1) in place of M,we get;

$\implies\sf{\dfrac{1+R}{2} -R=-2}$

$\implies\sf{1+R-2R=-4}$

$\implies\sf{1-R\:=\:-4}$

$\implies\sf{-R\:=\:-4-1}$

$\implies\sf{\cancel{-}R\:=\:\cancel{-}5}$

$\implies\sf{\red{R\:=\:5}}$

Putting the value of R in equation (1), we get;

$\implies\sf{M\:=\:\dfrac{1+5}{2} }$

$\implies\sf{M\:=\:\cancel{\dfrac{6}{2} }}$

$\implies\sf{\red{M\:=\:3}}$

Thus,

$\bf{\Large{\boxed{\sf{The\:Number\:is\:10(3)+5\:=\:30+5=35}}}}}}$