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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

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