Question

The sum of the digit of a two digit number is 9.The number obtained by reversing the digit is 9 less than the original number. Find the number.

Answer 1

$\sf\large\underline{Let:}$

• $\rm{The\: ones\: digit=x}$
• $\rm{The\: tens\: digit=y}$
• $\rm{The\: Number=10y+x}$

$\sf\large\underline{To\: Find:}$

• $\rm{The\: Number=?}$

$\sf\large\underline{Solution:}$

$\sf\underline{Given,\:in\: case\:1:}$

$\rm{\implies Sum\:of\:2\: digits=9}$

$\rm{\implies x+y=9}$

$\rm\purple{\implies x+y=9------(i)}$

$\sf\underline{Given,\:in\: case\:1:}$

$\rm{The\:number\:obtained\:by\:reversing\:the\:digit\:is\:9\:less\:than\: the \:original \:number}$

$\rm{\implies 10y+x-9=10x+y}$

$\rm{\implies 10x-x+y-10y=-9}$

$\rm{\implies 9x-9y=-9}$

• Dividing by 9 on both sides

$\rm\purple{\implies x-y=-1------(ii)}$

• Now, solving equation 1 and 2 here]

$\rm{\implies x+y=9}$

$\rm{\implies x-y=-1}$

• Now, adding equation here]

$\rm{\implies 2x=8}$

$\rm\red{\implies x=4}$

• Putting the value of x=4 in eq 1]

$\rm{\implies x+y=9}$

$\rm{\implies 4+y=9}$

$\rm{\implies y=9-4}$

$\rm\red{\implies y=5}$

$\sf\large{Hence,}$

$\rm{\implies The\: Number=10y+x}$

$\rm{\implies The\: Number=10\times5+4}$

$\rm{\implies The\: Number=50+4}$

$\rm\purple{\implies The\: Number=54}$

Answer 2

Question:

The sum of the digit of a two digit number is 9.The number obtained by reversing the digit is 9 less than the original number. Find the number.

• suppose that the number=10y+x

By solving we get

The value of ones digit=4

The value of ten's digit=5

• Now substitute value

=>10*5+4

=>50+4

=>54

Therefore, the orfinal number is 54