Question

The sum of a two digit number and the number obtained by interchanging the digits is 132. If the two digits differ by 2. Let the ten's digit be x and unit digit be y then the two digit number in x and y is​

Answer 1

Answer

Let unit's digit =y and the ten's digit =x

So, the original number =10x+y

After interchanging the digits, New number =x+10y

The sum of the number =10x+y

The sum of the digit =x+y

According to the question, (10x+y)+(x+10y)=132

⇒11x+11y=132

⇒11(x+y)=132

⇒x+y=12…(i)

and 10x+y+12=5(x+y)

⇒10x+y+12=5x+5y

⇒10x−5x+y−5y=−12

⇒5x−4y=−12…(ii)

From Eq. (i), we get x=12−y…( iii )

On substituting the value of x=12−y in Eq. (ii), we get

5(12−y)−4y=−12

⇒60−5y−4y=−12

⇒−9y=−12−60

⇒−9y=−72

⇒y=8

On putting the value of y=8 in Eq. (iii), we get

x=12−8=4

So, the Original number =10x+y

=10×4+8

=48

Hence, the two digit number is 48.