Question

the sum of a digit of 2 digit number is 12.the number got by interchanging the digit is 36 more than the original number. what is the number?​

Answer 1

$\underline{ \underline{ \Large \pmb{\mathit{ {Given:}} }} }$

• The sum of a digit of 2 digit number is 12.

• The number got by interchanging the digit is 36 more than the original number.

$\underline{ \underline{ \Large \pmb{\mathit{ {To \: calculate:}} }} }$

• The original number.

$\underline{ \underline{ \Large \pmb{\mathit{ {Calculation:}} }} }$

As it is a two digit number, so let us assume the original number as 10x + y. Where,

• x = tens digit.

• y = ones digit

As per the given question,

$\longrightarrow \sf { x + y = 12}$

Since, the sum of a digit of 2 digit number is 12.

Let it be the equation (i).

From this equation,

$\longrightarrow \sf { x= 12 - y}$

Also, the number got by interchanging the digit is 36 more than the original number.

→ Original number = 10x + y

→ Interchanged number = 10y + x

Linear equation formed,

$\longrightarrow \sf {10y +x = 36 + 10x + y }$

Solving further by using transposition method.

$\longrightarrow \sf {10y -y +x = 36 + 10x }$

$\longrightarrow \sf {9y +x = 36 + 10x }$

$\longrightarrow \sf {9y = 36 + 10x -x }$

$\longrightarrow \sf {9y = 36 + 9x }$

Substituting the value of x from equation (i).

$\longrightarrow \sf {9y = 36 + 9(12-y) }$

$\longrightarrow \sf {9y = 36 + 108 - 9y }$

$\longrightarrow \sf {9y +9y= 36 + 108 }$

$\longrightarrow \sf {18y= 144}$

$\longrightarrow \sf {y= \dfrac{144}{18}}$

$\longrightarrow\boxed{ \sf {y= 8}}$ ★

Also, from the equation (i) :-

$\longrightarrow \sf { x= 12 - y}$

$\longrightarrow \sf { x= 12 - 8}$

$\longrightarrow\boxed{ \sf {x= 4}}$ ★

Henceforth, value of x is 4 and y is 8. So,

$\longrightarrow \sf { Original \: Number= 10x + y}$

$\longrightarrow \sf { Original \: Number= 10(4) + 8}$

$\longrightarrow \sf { Original \: Number= 40 + 8}$

$\longrightarrow\boxed{\pmb{ \rm \red { Original \: Number= 48}}}$

Therefore, the original number is 48.