Question

sum of digits of a number is 6. if 36 is added to the number, its digits are reversed. determine the number

Answer 1

Let the one's digit be x and ten's digit be y.
Then the number becomes = 10 y + x

According to the question,

x + y = 6 --> ( i )

10 y + x + 36 = 10x + y

10y - 10x + x- y = - 36

9y - 9 x = - 36

9 ( y - x ) = - 36

y - x = - 36 / 9

y - x = - 4

x - y = 4 --> ( ii )

Adding both equations,

x + y + x - y = 6 + 4

2x = 10

x = 10 / 2 = 5

x = 5

Putting value of x in Eqn ( i ),

x + y = 6

5 + y = 6

y = 6 - 5 = 1

y = 1

Number = 10y + x

Number = 10 ( 1 ) + 5

Number = 15