Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the original number, it's digits are interchanged. Find the original number

Answer 1

Answer:

Step-by-step explanation:

Hope this help u

Answer 2

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

Original Number = 63

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

GiVeN :

• A number consists of two digits whose sum is 9.
• If 27 is subtracted from the original number, it's digits are interchanged.

To FiNd :

• The Original Number

SoLuTiOn :

Let the digit at the tens place be x.

Let the digit at the units place be y.

Original Number = 10x + y

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

• Sum of digits = 9

Constituting it mathematically,

$\implies$$\sf{x\:+\:y\:=9}$ ----> (1)

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

• When 27 is subtracted from the original number it's digit are interchanged.

Altered Number = 10y + x

Constituting it mathematically,

$\implies$$\sf{10x\:+\:y\:-\:27\:=\:10y\:+\:x}$

$\implies$$\sf{10x\:-\:x\:-\:27\:=\:10y\:-\:y}$

$\implies$$\sf{9x\:-\:27\:=\:9y}$

$\implies$$\sf{9x\:-\:9y\:=\:27}$

$\implies$$\sf{9(x-y)\:=\:27}$

$\implies$$\sf{x\:-\:y\:=\:{\dfrac{27}{9}}}$

$\implies$$\sf{x\:-\:y\:=\:3}$ ----> (2)

Solve equation 1 and equation 2 simultaneously by elimination method.

Add equation 1 to equation 2,

x + y = 9

x - y = 3

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$\implies$2x = 12

$\implies$$\sf{x\:=\:{\dfrac{12}{2}}}$

$\implies$$\sf{x\:=\:6}$

Substitute x = 6 in equation 1,

$\implies$$\sf{x\:+\:y\:=\:9}$

$\implies$$\sf{6\:+\:y\:=\:9}$

$\implies$$\sf{y\:=\:9\:-\:6}$

$\implies$$\sf{y\:=\:3}$

$\bold{\large{\boxed{\red{\rm{Tens\:digit\:=\:x\:=\:6}}}}}$

$\bold{\large{\boxed{\red{\rm{Units\:digit\:=\:y\:=\:3}}}}}$

$\bold{\large{\boxed{\red{\rm{Original\:Number\:=\:10x\:+\:y\:=\:10\:\times\:6\:+\:3\:=\:60\:+\:3\:=\:63}}}}}$