Question

4. Sum of digits of a two digit number is 12. When we interchange the digits, it is found that the resulting new number is smaller than the original number by 36. What is the original number?​

Answer 1

Answer:—

Original Number = 84

$\bold{\underline{\underline{step \: by \: step \: explanation:}}}$

Given:—

→ Sum of digits of a two digit number is12.

On interchange the digits, it is found that the resulting new number is smaller than the original number by 36.

To find:—

→ The original number

Solution:—

→ Let the digit in the tens place be x.

→ Let the digit in the units place be y.

•°• Original Number = 10x + y

$\bold{\underline{\underline{As\:per\:the\:first\:condition:}}}$

Sum of digits of a two digit number is 12.

Constituting it mathematically,

$\rightarrow\bold{x+y=12}x---> (1)$

$\bold{\underline{\underline{As\:per\:the\:second\:condition:}}}$

The resulting new number is smaller than the original number by 36, on interchanging.

Reversed Number = 10y + x

Constituting the condition mathematically,

$\rightarrow \bold{10y+x=10x+y-36}$

$\rightarrow \bold{10y-y=10x-x-36}$

$\rightarrow\bold{9y=9x-36}$

$\rightarrow \bold{9x-36=9y}$

$\rightarrow \bold{9x-9y=36}$

$\rightarrow \bold{9(x-y) =36}$

$\rightarrow\bold{x-y ={\dfrac{36}{9}}}$

$\rightarrow \bold{x-y=4} ---> (2)$

Solve equation 1 and equation 2 simultaneously by elimination method.

Add equation 2 to equation 1,

x + y = 12

x + y = 12 x - y = 8

----------------

2x = 16

$\rightarrow \bold{x={\dfrac{16}{2}}}$

$\rightarrow \bold{x=8}$

Substitute x = 8 in equation 1,

$\rightarrow \bold{x+y=12} ---> (1)$

$\rightarrow \bold{8+y=12}$

$\rightarrow\bold{y=12-8}$

$\rightarrow\bold{y=4}$

$\bold{\sf{\orange{Tens\:digit\:x\:=\:8}}}$

$\bold{\sf{\blue{Units\:digit\:y\:=\:4}}}$

$\bold{\boxed{\sf{\purple{Original\:Number\:=\:10x+y\:=10\times\:8+4\:=80+4=84}}}}$

@vikramjeeth