Question

the sum of a two digit no is 12.If the new number formed by reversing its digitsis greater than the original number by 54.Find the number

Answer 1

39

Explanation:

Let x be tens place digit and y be units place digit.

Therefore, required number = 10x + y

On reversing the digits number so obtained = 10y + x

According to the given information:

10y + x = 10x + y + 54

10y + x - 10x - y = 54

9y - 9x = 54

9(y - x) = 54

y - x = 54/9

y - x = 6

y = x + 6...... (1)

Since, sum of the digits is 12.

Therefore, x + y = 12....(2)

From equations (1) & (2)

x + x + 6 = 12

2x = 12 - 6

2x = 6

x = 6/2

x = 3

y = x + 6 = 3 + 6 = 9...[from eqn (2)]

10x + y = 10*3 + 9 = 30 + 9 = 39

Thus, the required number is 39.