Question

the digit in the tens place of a two digit number is three times that in the ones place of the digits are reversed the new number will be 36 less than the original find the number

Answer 1

Solution :

$\bf{\purple{\underline{\bf{Given\::}}}}$

The digit in the tens place of a two digit numbers is three times that in ones place of the digits are reversed the new number will be 36 less than the original number.

$\bf{\purple{\underline{\bf{To\:find\::}}}}$

The number.

$\bf{\purple{\underline{\bf{Explanation\::}}}}$

Let the one's place be r

Let the ten's place be m

$\boxed{\bf{The\:original\:number=10m+r}}}}$

$\boxed{\bf{The\:reversed\:number=10r+m}}}}$

A/q

$\longrightarrow\sf{m=3r................(1)}$

&

$\longrightarrow\sf{10m+r-36=10r+m}\\\\\longrightarrow\sf{10m-m+r-10r=36}\\\\\longrightarrow\sf{9m-9r=36}\\\\\longrightarrow\sf{9(m-r)=36}\\\\\longrightarrow\sf{m-r=\cancel{\dfrac{36}{9} }}\\\\\longrightarrow\sf{m-r=4}\\\\\longrightarrow\sf{3r-r=4\:\:[from(1)]}\\\\\longrightarrow\sf{2r=4}\\\\\longrightarrow\sf{r=\cancel{\dfrac{4}{2} }}\\\\\longrightarrow\sf{\orange{r=2}}$

Putting the value of r in equation (1),we get;

$\longrightarrow\sf{m=3(2)}\\\\\longrightarrow\sf{\orange{m=6}}$

Thus;

$\underbrace{\sf{The\:original\:number\:=\big\lgroup10m+r\big\rgroup=10(6)+2=60+2=\boxed{62}}}}}$

Answer 2

$\huge\sf{Answer:}$

☆ Given:

⇏ The digit in the tens place of a two digit number is three times that in the ones place of the digits are reversed the new number will be 36 less than the original.

☆ Find:

⇏ Find the number.

☆ According to the question:

⇏ Let us assume 'x' and 'y' as ones and tens place, Let (10y + x) and (10x + y) bethe original number and reversed number.

☆ Calculations:

⇏ $\sf x = 3y - Equation \: (1)$

⇏ $\sf [(10x + y) - 36] = (10y + x)$

⇏ $\sf (9x - 9y) = 36$

⇏ $\sf 9 (x - y) = \cancel{ \dfrac{36}{9}}$

⇏ $\sf (x - y) = 4$

☆ Adding values from equation (1), we get:

⇏ $\sf 3y - y = 4$

⇏ $\sf 2y = \dfrac{4}{2}$

⇏ $\sf y = 2$

☆ Finding the number by adding the values, we get:

⇏ $\sf x = (3 \times 2)$

⇏ $\sf x = 6$

⇏ $\sf (10x + y) = (10 \times 6) + 2$

⇏ $\sf 60 + 2$

Therefore, original number = ${\sf{\underline{\boxed{\green{\sf{62}}}}}}$