The sum of a two digit number and the number by interchanging the no is 132 if 12 is added to number the new becomes 5 times the sum of digit. Find the number?
Let the number be xy=10x+y
Number obtained by interchanging the digits =yx=10y+x
From the given information, we have:
10x+y+10y+x=132
⇒11x+11y=132
⇒x+y=12 ... (1)
Also, we have:
⇒10x+y+12=5(x+y)
⇒10x+y+12−5x−5y=0
⇒5x−4y+12=0 ... (2)
Multiplying (1) by 4, we get
⇒4x+4y−48=0 ... (3)
Adding (2) and (3), we get,
⇒9x−36=0
∴x=4
So, y=12−4=8
Thus, the number is 48.