Question

A number consisting of two-digits, is 7 times the sum of its digits. When 27 is subtracted from the number, the digits are reversed. Find the number.

Answer 1

Let x is the tenth digit and y is unit digit.
then the number is 10x+y.

The number is 7 times the sum of the digits. So,
10x+y = 7(x+y)
⇒10x-7x = 7y-y
⇒3x = 6y
⇒x=2y

Also (10x+y)-27 = 10y+x
⇒10x-x = 10y-y+27
⇒9x = 9y +27
⇒9×2y = 9y + 27
⇒18y - 9y = 27
⇒9y = 27
⇒ y = 27/9 = 3
x = 2y = 6

The number is 10x+y = 63

Answer 2

Digit in Tens place = x 
Digit in units place = y
The number is 10x + y
The number is 7 times its sum of digits
10x + y = 7(x+y) 
10x + y = 7x + 7y
3x - 6y =0
3x = 6y
x = 2y .................(1)
If 27 is subtracted from the number, the digits are reversed.

10x + y - 27 = 10y + x
⇒ 9x - 9y = 27
⇒ x - y = 3    ........(2)

Solving equations (1) and (2)
 We get, x = 6 and y = 3

The number is 63