Question

sum of digit of a two digit number is 11 when the digit are interchanged the new number formed is less than the original number by 27 find the original number​

Answer 1

$\large{\underline{\underline{ \bf{⎆Question:-}}}}$

• Sum of digit of a two digit number is 11 when the digit are interchanged the new number formed is less than the original number by 27 find the original number .

$\large{\underline{\underline{ \bf{☂ Solution:-}}}}$

$\small{\underbrace{\overbrace{\color{green}{➥Given}}}}$

• Sum of two digit number = 11
• After interchanging the new number formed is less than the original number by 7

$\small{\underbrace{\overbrace{\color{green}{➥To \: find }}}}$

• The original number found after interchanging .

$\small\underline{\overline{\mid{\bold{\red{➥According \: to \: the \: question-}}\mid}}}$

Let suppose 'a' be at the one's place digit and 'b' be at tenth place digit.

$\small\underline{\overline{\mid{\bold{\red{➥So-}}\mid}}}$

➭Original number :

$\large{\underbrace{{\color{bold}{10b \: + \: a}}}}$

➭After interchanging :

$\large{\underbrace{{\color{bold}{10a \: + \: b}}}}$

$\small\underline{\overline{\mid{\bold{\red{➥Now-}}\mid}}}$

➭Sum of the digits is 11 :

$\small\fbox\green{x + y = 11 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (i) }$

➭Difference of orginal number and interchanged number is 27

$\small\fbox\green{10y + x - 10x - y = 27 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (ii) }$

➭Solving equations i and ii , we get :

$\small\fbox\pink{x + y = 11 }$

$\small\fbox\pink{x - y = - 27 }$

➭Solving these two equations , we get :

$\underline{ \boxed{ \sf{x = 4 }}}$

$\underline{ \boxed{ \sf{y = 7 }}}$

$\small\underline{\overline{\mid{\bold{\red{Therefore-}}\mid}}}$

✰ Original Number : 74

✰ Interchanged Number : 47