Question

The sum of a two-digit number and the number formed by interchanging the digits is 132. If 12 is added to the number, the new number becomes 5 times the sum of digits. Find the number.

Answer 1

let the two digit no. be 10x + y
and the no. when reversed be 10y + x
according to the question :
10x + y + 10y + x = 132
11x + 11y = 132
taking 11 common
11(x + y ) = 132
x + y = 12 ----------- 1)
lets do the second part
Now,
10x + y + 12 = 5(x + y)
10x + y + 12 = 5x + 5y
5x + 12 = 4y
4y - 5x = 12 ------ 2)
substituting y = 12 - x in equation 2)
4( 12 - x ) - 5x = 12
48 - 4x - 5x = 12
48 - 12 = 9x
36 = 9x
x = 4
x + y = 12
4 + y = 12
y = 8
so the no. is 48


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Answer 2

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