Question

the sum of the digits in a 2-digit number is 10. When we reverse the digits ,then the difference of this number and the original number become 36. find the number​

Answer 1

Question :

• The sum of the digits in a 2-digit number is 10.

• When we reverse the digits ,then the difference of this number and the original number become 36.

Find the number

Solution :

Let us assume that the original number is xy .

The sum of the digits of this two digit number is 10.

> x + y = 10

On reversing the digits , the new number becomes yx .

The difference between the new and original numbers is 36.

> yx - xy = 36

> 10y + x - 10x - y = 36

> 9y - 9x = 36

> y - x = 4

Adding this with the first equation

• x + y = 10

• y - x = 4

> 2y = 14

> y = 7

> x = 3.

Answer - The required number is 37.

______________________________________

Answer 2

• $\LARGE\boxed{\sf{\blue{Number = 37}}}$

Explanation :

$\underline{\red{\bigstar}{\underline{\bf{Question}}}\red{\bigstar}}$

• The sum of the digits in a 2 - digit number is 10. When we reverse the digits , then the difference of this number and the original number become 36. Find the number.

$\underline{\red{\bigstar}{\underline{\bf{Solution}}}\red{\bigstar}}$

• Let the one's digit = x
• And, ten's digit = y

★ According to first condition :-

$\qquad\leadsto\quad\sf x + y = 10 \qquad\qquad\bigg\lgroup \sf{eq^{n}} \:(1) \bigg\rgroup$

★ According to second condition :-

$\qquad\leadsto\quad\sf Original\:number = 10y + x$

$\qquad\leadsto\quad\sf Reversed\:number = 10x + y$

A/q,

$\qquad\leadsto\quad\sf (10x + y) - (10y + x) = 36$

$\qquad\leadsto\quad\sf 10x + y - 10y - x = 36$

$\qquad\leadsto\quad\sf 10x - x - 10y + y = 36$

$\qquad\leadsto\quad\sf 9x - 9y = 36$

$\qquad\leadsto\quad\sf 9(x - y) = 36$

$\qquad\leadsto\quad\sf x - y = \dfrac{36}{9}$

$\qquad\leadsto\quad\sf x - y = \dfrac{\cancel{36}}{\cancel{9}}$

$\qquad\leadsto\quad\sf x - y = 4 \qquad\qquad\:\bigg\lgroup \sf{eq^{n}} \:(2) \bigg\rgroup$

★ Adding eqⁿ (1) and eqⁿ (2) :-

$\qquad\rightarrow\quad\sf (x + y) + (x - y) = 10 + 4$

$\qquad\rightarrow\quad\sf x + y + x - y = 14$

$\qquad\rightarrow\quad\sf x + x + y - y = 14$

$\qquad\rightarrow\quad\sf 2x + \cancel{y} - \cancel{y} = 14$

$\qquad\rightarrow\quad\sf 2x = 14$

$\qquad\rightarrow\quad\sf x = \dfrac{14}{2}$

$\qquad\rightarrow\quad\sf x = \dfrac{\cancel{14}}{\cancel{2}}$

$\qquad\rightarrow\quad\bf{x = \red{7}}$

★ Putting value of x in eqⁿ (1) :-

$\qquad\rightarrow\quad\sf 7 + y = 10$

$\qquad\rightarrow\quad\sf y = 10 - 7$

$\qquad\rightarrow\quad\bf{y = \red{3}}$

Hence,

$\longrightarrow\qquad\sf Number = 10y + x$

★ Putting value of x and y :-

$\longrightarrow\qquad\sf Number = 10\:\times\:3 + 7$

$\longrightarrow\qquad\sf Number = 30 + 7$

$\longrightarrow\qquad\bf{Number = \red{37}}$

$\quad\red{\therefore}\:{\underline{\rm{Hence,\:number\:is\:\bf{37}\:\rm{respectively}.}}}$