Question

The sum of a 2 digit number is 11. If the number obtained by reversing the digit is 9 less than the original number, what is the number?​

Answer 1

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Question}}}}}}}}$

The sum of a 2 digit number is 11. If the number obtained by reversing the digit is 9 less than the original number, what is the number?

${\huge{\bold{\purple{\bigstar{\boxed{\boxed{\bf{Solution}}}}}}}}$

let the number be 10x + y

${\bold{\blue{\boxed{\bf{Given }}}}}$

• x + y = 11
• 10x + y = 9 + 10y + x

${\bold{\blue{\boxed{\bf{to\: find }}}}}$

• the correct number

${\bold{\blue{\boxed{\bf{Solution}}}}}$

x + y = 11 -------------(i)

10x + y = 9 + 10y + x

10x - x + y -10y = 9

9x - 9y = 9

9(x-y)= 9

x-y = 1-----------(ii)

• adding eq (i) and (ii)

x + y + x - y = 11 + 1

2x = 12

x = 6

• putting value of x in eq (i)

x+y = 11

6+y = 11

y = 11-6

y = 5

required no. = 10x + y = 10 * 6 + 5 = 60 + 5 = 65

${\bold{\blue{\boxed{\bf{required\:no. = 65 }}}}}$

____________________________❤

THANK YOU ❤

Answer 2

★$\bold{\underline{\underline{\rm{\red{Question:-}}}}}$

• The sum of a 2 digit number is 11. If the number obtained by reversing the digit is 9 less than the original number, what is the number?

★$\bold{\underline{\underline{\rm{\pink{Answer:-}}}}}$

• The number is 65.

★$\bold{\underline{\underline{\rm{\purple{To find:-}}}}}$

• The number according to the question.

★$\bold{\underline{\underline{\rm{\blue{Given:-}}}}}$

• Sum of a 2 digit number is 11.
• The no. obtained by reversing the digit is 9 less than the original no.
• $\sf \: x + y = 10... \{1 \}$

★$\bold{\underline{\underline{\rm{\orange{Explanation:-}}}}}$

• Let the 2 digit number be $: \implies \sf \:10x + y$
• Number obtained by reversing the digit be $:\implies \sf \:10y + x$

$\sf \: According \: to \: the \: question,$

$\\ \\ : \implies \sf \: \: \: \: \: (10x+y)-(10y+x)=9$

$\ : \implies \sf \: \: \: \: \: 10x + y - 10y - x = 9$

$: \implies \sf \: \: \: \: \: 9x - 9y = 9 \\ \\ \\ : \implies \sf \: \: \: \: \: 9(x - y) = 9 \\ \\ \\: \implies \sf \: \: \: \: \: x - y = 9 - 9 \\ \\ \\ : \implies \sf \: \: \: \: \: x - y = 1 \\ \\ \\ : \implies \sf \: \: \: \: \: x + y + x - y = 11 + 1 \\ \\ \\ : \implies \sf \: \: \: \: \: 2x = 12 \\ \\ \\ \red : \implies \sf \: \bold{\red{\boxed{\bigstar{\sf{x = 6}}}}}$

$\\ \\ \sf \: Substitute \: the \: value \: \: x \: in \: equation \: 1$

$\\ : \implies \sf \: \: \: \: \: 6 + y = 11 \\ \\ \\: \implies \sf \: \: \: \: \:y = 11 - 6 \\ \\ \\ \orange : \implies \sf \: \: \: \: \bold{\orange{\boxed{\bigstar{\sf{y = 5 \: }}}}}$

$\\ \large{\underline{\underline {\sf{\pink{Original \: number:- \: }}}}} \: \\ \\ \implies10\times6+5 \\ \\ \implies60+5 \\ \\ \implies65$

$\sf \therefore \: \: The \: required \: no. \: is \: \huge \red6 \red5.$