Question

The sum of the digits of a two digit number is equal to 1/8 of the number . If the digits are reversed , the new number is 45 less than the original number. Find the original number .

Answer 1

Let the number be 10b + a where a is the digit at the ones place and b is the digit at the tens place.

Now given that,

a + b = 1/8*(10b + a)......... (1)
Also given that,

10a + b = (10b + a) - 45.......(2)

Now we expand equation (1),


8(a + b) = 10b + a
=> 8a + 8b = 10b + a
=> 7a = 2b
=> b = 7/2*a


Putting the value of b as 7/2*a in equation (2),

10a + 3.5a = 35a + a - 45
=> 13.5a = 36a - 45
=> 36a - 13.5a = 45
=> 22.5 a = 45
=> a = 2

b = 7/2*a = 7

The original number was 10b + a = 72