The sum of a two digit number and the number formed by interchanging the digit is 132 .if 12 is added to the number ,the number becomes 5 times the sum the digit .find the number
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let the number be xy=10x+y
the number obtained by interchanging the digits is 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)
5x-4y+12=0. _2
Multiplying 1 by4 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 is48.
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