Question

the sum of the digits number is 10
the number obtained by inchanging the digits exceed the original number by 36 . find the original number ​

Answer 1

Given:

• sum of the digits = 10

• number obtained by inchanging the digits exceed the original number = 36

To Find:

the original number

Solution:

Let the number at one's place be "x"

then the number at ten's place will be = 10 - x

original number = 10x + y

$⟹10(10 - x) + x$

$⟹100 - 10x + 10$

$⟹100 - 9x$

New number = 10y + x

$⟹10x + (10 - x)$

$⟹9x + 10$

☆ A/Q

New number - Original number = 36

$⟹9x + 10 - (100 - 9x) = 36$

$⟹9x + 10 - 100 + 9x = 36$

$⟹18x - 90 = 36$

$⟹18x = 36 + 90$

$⟹x = \frac{126}{18} = 7$

$⟹x = 7$

∴ the original number = 10x + y

$⟹10(10 - 7) + 7$

$⟹100 - 70 + 7$

$⟹37$

Hence:

${\boxed{\sf{\red{the\: original\: number\:is\:37}}}}$

Answer 2

Step-by-step explanation:

sum of the digits = 10

• number obtained by inchanging the digits exceed the original number = 36

To Find:

the original number

Solution:

Let the number at one's place be "x"

then the number at ten's place will be = 10 - x

original number = 10x + y

⟹10(10 - x) + x⟹10(10−x)+x

⟹100 - 10x + 10⟹100−10x+10

⟹100 - 9x⟹100−9x

New number = 10y + x

⟹10x + (10 - x)⟹10x+(10−x)

⟹9x + 10⟹9x+10

☆ A/Q

New number - Original number = 36

⟹9x + 10 - (100 - 9x) = 36⟹9x+10−(100−9x)=36

⟹9x + 10 - 100 + 9x = 36⟹9x+10−100+9x=36

⟹18x - 90 = 36⟹18x−90=36

⟹18x = 36 + 90⟹18x=36+90

⟹x = \frac{126}{18} = 7⟹x=

18

126

=7

⟹x = 7⟹x=7

∴ the original number = 10x + y

⟹10(10 - 7) + 7⟹10(10−7)+7

⟹100 - 70 + 7⟹100−70+7

⟹37⟹37

Hence:

{\boxed{\sf{\red{the\: original\: number\:is\:37}}}}

theoriginalnumberis37