Question

The sum of a two digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3, find the number.
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Answer 1

Let the unit's place digit be x .

The ten's place digit be y .

$\boxed {\sf{ \therefore \: Original \: number = x + 10y}}$

$\boxed { \sf{The \: no. \: obtained \: by \: reversing \: the \: digits = 10x + y}}$

According to the question ,

$\sf{Original \: no. + Reversed \: no. \: = 99}$

$: \implies \sf{ (x + 10y) + (10x + y) = 99}$

$: \implies \sf{11x + 11y = 99}$

$: \implies \sf{x + y = 9}$

$: \implies \sf{x = 9 - y.....(i)}$

$\sf{The \: difference \: of \: the \: digits = 3 } \: \: \: \: \: (Given)$

$: \implies \sf{x - y = 3.......(ii)}$

On putting the value of x in equation ( ii ) ,we get :

$: \implies \sf{x - y = 3}$

$: \implies \sf{(9 - y) - y} = 3$

$: \implies \sf{9 - 2y = 3}$

$: \implies \sf{ - 2y = 3 - 9}$

$: \implies \sf{2y = 6}$

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

$: \implies \sf{y = 3}$

Putting the value of y in equation ( i ),we get:

$\sf{x = 9 - y}$

$\rightarrow \sf{x = 9 - 3}$

$\rightarrow \sf{x = 6}$

Hence,

The number = x + 10 y ⇒ 6 + 10 × 3 ⇒ 6 + 30 ⇒ 36.

Answer 2

${\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}}$

${\pink{\underline{\blue{The\:number\:is:36.\:or\:63}}}}$

_________________________________________

$\sf\large\underline\pink{Given:}$

➨The sum of a two digit number and the number obtained by reversing the order of its digits is 99.

➨The digits differ by 3.

_________________________________________

$\sf\large\underline\blue{To \ Find}$

The number .

_________________________________________

${\purple{\underline{\underline{\blue{\boxed{\boxed{\pink{\star{\sf Solution:}}}}}}}}}$

Let the 2 digits be of the m , m. respectively

➛ 2 digit number = 10m + n.

2 digit number obtained by ususing the digit

= 10n + m

∴ ( 10m + n ) + ( 10n + x ) = 99

⇒11m + 11n = 99

⇒ m + n = 9 .................. ( 1 )

By the second condition,

➛ m - n = 3 ................... ( 2 )

On adding equation ( 1 ) and ( 2 )

m + n = 9

+

m - n = 3

_____________

2m = 12

m = 12 / 2

∴ m = 6

putting m = 6 in ⟶ equation ( 1 )

➞ 6 + n = 9

➞ n = 9 - 6

∴ n = 3

Hence, Number is :

➞ 10m + n = 63

or ,

➞ 10n + m = 36.

Therefore, The number is 63 or 36.