Question

a number consists of two digits whose sum is 8 if 18 is added to the number its digits are reversed find the number​

Answer 1

Answer:

Explanation:

Given :-

A number consists of two digits whose sum is 8.

If 18 is added to the number its digits are reversed.

To Find :-

The Number

Solution :-

Let digits be x and y

Number = 10x + y

Reversed Number = 10y + x

According to the question,

⇒  x + y = 8 .........(i)

 

⇒ 10x + y + 18 = 10y + x

⇒ 9x - 9y = -18

⇒  x - y = -2  ........(ii)

Adding Eq (i) and (ii), we get

⇒ x = 3

⇒ y = 5

Hence, the number is 35.

Answer 2

$\bold{\underline{\underline{\huge{\sf{AnsWer:}}}}}$

Original Number = 35

$\bold{\underline{\underline{\huge{\sf{StEp\:by\:stEp\:explanation:}}}}}$

GiVeN :

• A number consists of two digits whose sum is 8
• When 18 is added to the number its digits are reversed

To FiNd :

• The Number

SoLuTiOn :

Let the digit at the tens place be x

Let the digit at the units place be y

Original Number = 10x + y

$\sf{\underline{\underline{As\:PeR\:tHe\:FiRsT\:cOnDiTiOn:}}}$

• Sum of the digits = 8

Constituting it mathematically,

$\longrightarrow$ $\sf{x+y=8}$ ---> (1)

$\sf{\underline{\underline{As\:PeR\:tHe\:SeCoNd\:cOnDiTiOn:}}}$

• When 18 is added to the number its digits are reversed.

Altered Number = 10y + x

Constituting second condition mathematically,

$\longrightarrow$ $\sf{10x\:+\:y\:+\:18\:=\:10y\:+\:x}$

$\longrightarrow$ $\sf{10x\:-\:x\:+\:18\:=\:10y\:-\:y}$

$\longrightarrow$ $\sf{9x\:+18\:=\:9y}$

$\longrightarrow$$\sf{9x\:-\:9y\:=\:-18}$

$\longrightarrow$ $\sf{9(x\:-\:y\:)\:=\:-\:18}$

$\longrightarrow$ $\sf{x\:-\:y\:=\:{\dfrac{-18}{9}}}$

$\longrightarrow$ $\sf{x\:-\:y\:=\:-\:2}$ ---> (2)

Solve equation 1 and equation 2 simultaneously by elimination method.

Add equation 2 to equation 1,

$\sf{x\:+\:y\:=\:8}$

$\sf{x\:-\:y\:=\:-2}$

______________

$\longrightarrow$$\sf{2x\:=\:6}$

$\longrightarrow$$\sf{x\:=\:{\dfrac{6}{2}}}$

$\longrightarrow$$\sf{x\:=\:3}$

Substitute x = 3 in equation 1,

$\longrightarrow$ $\sf{x\:+\:y\:=\:8}$

$\longrightarrow$$\sf{3\:+\:y\:=\:8}$

$\longrightarrow$$\sf{y\:=\:8\:-\:3}$

$\longrightarrow$$\sf{y\:=\:5}$

$\bold{\large{\boxed{\sf{\purple{Tens\:digit\:=\:x\:=\:3\:}}}}}$

$\bold{\large{\boxed{\sf{\purple{Units\:digit\:=\:y\:=\:5\:}}}}}$

$\bold{\large{\boxed{\sf{\purple{Original\:Number\:=\:10x\:+\:y\:=\:10\:\times\:3\:+\:5\:=\:30\:+\:5\:=35}}}}}$