Question

A number consisting of 2 digits is equal to 7 times the sum of its digits. When 27 is subtracted from the number, the digits interchange places. Find the number.

Answer 1

Let the digit at tens place be = x
Let the digit at ones place be = y
Therefore...
Original No. = 10x + y
No. With digits reversed = 10y + x

A.T.Q...

10x + y = 7( x + y)
10x + y = 7x + 7y
10x - 7x + y - 7y = 0

Therefore........ 3x - 6y = 0 ------------- Equation (1)


And,

10x + y - 27 = 10y + x
10x - x + y - 10y = 27
9x - 9y = 27 ( Dividing the whole equation by 3 )

Therefore.......... 3x - 3y = 9 ------------- Equation (2)

Subtracting eq 2 from eq 1

3x - 6y - ( 3x - 3y ) = 0 - 9
3x - 6y - 3x + 3y = -9
-3y = -9
y = -9/-3

Therefore........ y = 3

3x - 3y = 9
3x - 9 = 9
3x = 18
x = 18/3

Therefore......... x = 6

This implies......original no......... = 10x + y
= 60 + 3
= 63