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Question

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?

Solution
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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+125x5y=0
5x4y+12=0 ... (2)
Multiplying (1) by 4, we get
4x+4y48=0 ... (3)
Adding (2) and (3), we get,
9x36=0
x=4
So, y=124=8
Thus, the number is 48.

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