Question

The sum of the digits of a two digit number is 9. The number obtained by reversing the order of the digit of the given number exeeds by 27. Find the given number

Answer 1

AnSwer:

Let the two digit number be 10x+y.

According to the question,

Sum of the 2 digit number is 9. So,

$\sf \longmapsto \: \: x+y=9 - - - - (1)$

Also,

Number obtained by reversing the order of the digit of the given number exeeds by 27.

So,

$\sf \longmapsto \: \:10y+x=10x+y+27 \\ \\ \sf \longmapsto \: \:9x - 9y= - 27 \\ \\ \sf \longmapsto \: \:x - y= - 3 - - - - (2)$

Now,

Add eqn (1) and (2),

$\sf \: x+y=9 \\ \sf \: x - y= - 3$

_______________

$+ \: \: \: - \: \: \: = \: \: -$

$\longmapsto \sf \: \: 2x=6 \\ \\ \longmapsto \sf \: \: x=3 \\ \\ \sf \: and, \\ \\ \longmapsto \sf \: \:3+y=9 \\ \\ \longmapsto \sf \: \: y=6$

★ The number is =

$\longmapsto \sf \: \: 10x+y \\ \\\longmapsto \sf \: \:10(3) + 6 \\ \\ \longmapsto \sf \: \:30 + 6 \\ \\ \longmapsto \sf \: \:36$

Therefore, the number is 36.

Answer 2

$\sf{\huge{\mathfrak{\underline{\boxed{\pink{Solution}}}}}}$

let the 2 Digit number be 10x + y

• The sum of the digits of a two digit number is 9.

$\sf{\bold{\purple{x + y = 9 ------(i)}}}$

• The number obtained by reversing the order of the digit of the given number exeeds by 27.

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

$\\ \sf{10x - x + y - 10y + 27 = 0 }$

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

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

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

$\\ \sf{\bold{\purple{x - y = -3 ----(ii)}}}$

• adding eq i and ii

☞x + y + x - y = 9 + ( - 3)

☞2x = 9 - 3

☞2x = 6

☞x = 3

$\\ \sf{\bold{\boxed{\purple{x = 3 }}}}$

• value of y

☞ x + y = 9

☞3 + y = 9

☞y = 9 - 3

☞y = 6

$\\ \sf{\bold{\boxed{\purple{y = 6 }}}}$

• required number :-

☞ 10x + y

☞10 x 3 + 6

☞30 + 6

☞36

$\\ \sf{\bold{\boxed{\purple{\dag required\: number = \:36 }}}}$

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