Question

The sum of the digits of a two digit number is 15. If the number formed
by reversing the digits is less than the original number by 27. Find the
original number. ​

Answer 1

Given :

• The sum of the digits of a two digit number is 15.
• The number formed by reversing the digits is less than the original number by 27.

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

Case 1 :

$\mathtt{Ten's\:digit\:+\:Unit's\:digit\:=\:15}$

$\mathtt{x+y=15}$ ____(1)

Case 2 :

Reveresed Number → 10y + x

Equation :

➣ $\mathtt{10y+x=10x+y-27}$

➣ $\mathtt{10x+y-27=10y+x}$

➣ $\mathtt{10x-x=10y-y+27}$

➣ $\mathtt{9x=9y+27}$

➣ $\mathtt{9x-9y=27}$

Divide throughout by 9,

➣ $\mathtt{\cancel\dfrac{9}{9}x}$ $\mathtt{-\cancel\dfrac{9}{9}y}$ $\mathtt{=\cancel\dfrac{27\:\:^3}{9\:\:\:^1}}$

$\mathtt{x-y=3}$ ___(2)

Solve equation (1) and 2 to find the value of x and y.

Add equation 1 to equation 2,

➣ $\mathtt{x\:\cancel{+y}+x\:\cancel{-y}=15+3}$

➣ $\mathtt{2x=18}$

➣ $\mathtt{x\:=\:\cancel\dfrac{18}{2}}$

➣ $\mathtt{x=9}$

Substitute, x = 9 in equation 1,

➣ $\mathtt{x+y=15}$

➣ $\mathtt{y=15-x}$

$\mathtt{y=15-9}$

➣ $\mathtt{y=6}$

Original Number :

$\large{\boxed{\sf{\red{Ten's\:digit\:=\:x\:=\:9}}}}$

$\large{\boxed{\sf{\red{Unit's\:digit\:=\:y\:=\:6}}}}$

$\large{\boxed{\sf{\red{ Original\:Number\:=\:10x+y\:=\:10(9)\:+6\:=\:90\:+\:6=96}}}}$

Answer 2

Pls mark as brainliest answer