Question

plzzzz solve it...... ​

Answer 1

$\huge{\underline{\pink{\tt{Given,}}}}$

A Number Consists of Two Digits when the Number is Divided by the sum of Digit the Quotient is 7.

If 27 is Subtracted from the Number then the Digits Interchange their Place.

$\huge{\underline{\pink{\tt{To \ Find,}}}}$

The Two Digit Numbers

$\huge{\underline{\pink{\tt{Solution :}}}}$

$\longrightarrow$ Suppose the Digit at the One's Place be x

And, Suppose the Digit at the Ten's Place be y

Therefore,

The Two Digit Number - (10y + x)

The Interchange Number - (10x + y)

$\mapsto \underline{\underline{\purple{\mathfrak{According\:to\:the\:First\:Condition:}}}}$

A Number Consists of Two Digits when the Number is Divided by the sum of Digit the Quotient is 7.

$\longrightarrow \sf{\dfrac{10y + x}{x + y} = 7}$

$\longrightarrow \sf{10y + x = 7x + 7y}$

$\longrightarrow \sf{10y - 7y = 7x - x}$

$\longrightarrow \sf{3y = 6x}$

$\longrightarrow \sf{y = \dfrac{6x}{3}}}$

$\longrightarrow \boxed{\sf{y = 2x}}$...1)Equation

$\mapsto \underline{\underline{\purple{\mathfrak{According\:to\:the\:Second\:Condition:}}}}$

If 27 is Subtracted from the Number then the Digits Interchange their Place.

$\longrightarrow \sf{10y + x - 27 = 10x + y}$

$\longrightarrow \sf{10y - y - 9x = 27}$

$\longrightarrow \sf{9y - 9x = 27}$

║Now Put the Value of y From the First Equation ║

$\longrightarrow \sf{9(2x) - 9x = 27}$

$\longrightarrow \sf{18x - 9x = 27}$

$\longrightarrow \sf{9x = 27 }$

$\longrightarrow \sf{x = \dfrac{27}{9}}$

$\longrightarrow \boxed{\sf{x = 3}}$

Now Put the Value of x in First Equation :

$\longrightarrow \sf{y = 2x}$

$\longrightarrow \sf{y = 2(3)}$

$\longrightarrow \boxed{\sf{y = 6}}$

Therefore,

$\mapsto \boxed{\pink{\mathfrak{The\:Original\:Number = 10y + x = 10(6)+ 3 = 63}}}$

$\mapsto \boxed{\pink{\mathfrak{The\:Interchange\:Number = 10x + y = 10(3) + 6 = 36}}}$

$\rule{200}2$