Question

The sum of the digit of a two digit number is 8. if the digit are reversed, the new number increases by 18.
find the number

Answer 1

Explanation:

The number is 53.

Let the number be 10x+y.

Here x + y = 8 …(1)

10x+y - (10y+x) = 18 … (2)

(2) becomes 10x+y - 10y-x = 18 or

9x -9y = 18, or

x - y = 2 … (3)

x+y = 8 … (1). Add (1) and (3) to get

2x = 10, or x = 5. The y = 8–5 = 3

Hence the number is 53. The reverse is 35 and 53–35 = 18.

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Answer 2

Solution :

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

The sum of the digit of a two digit number is 8. If the digit are reversed, the new number increased by 18.

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

The number.

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

Let the ten's place be r

Let the one's place be m

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

A/q

$\longrightarrow\sf{r+m=8}\\\\\longrightarrow\sf{m=8-r..........................(1)}$

&

$\longrightarrow\sf{10m+r=10r+m+18}\\\\\longrightarrow\sf{10m-m+r-10r=18}\\\\\longrightarrow\sf{9m-9r=18}\\\\\longrightarrow\sf{9(m-r)=18}\\\\\longrightarrow\sf{m-r=\cancel{\dfrac{18}{9} }}\\\\\longrightarrow\sf{m-r=2}\\\\\longrightarrow\sf{8-r-r=2\:\:\:[from(1)]}\\\\\longrightarrow\sf{8-2r=2}\\\\\longrightarrow\sf{-2r=2-8}\\\\\longrightarrow\sf{-2r=-6}\\\\\longrightarrow\sf{r=\cancel{\dfrac{-6}{-2} }}\\\\\longrightarrow\sf{\pink{r=3}}$

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

$\longrightarrow\sf{m=8-3}\\\\\longrightarrow\sf{\pink{m=5}}$

Thus;

$\underbrace{\bf{The\:number=(10r+m)=10(3)+5=30+5=\boxed{35}}}}}$