Question

The sum of the digits of a three digit number is 12. if the digits are reversed, the number diminished by 396. find tge number

Answer 1

The three digits of the number are 5,6 and 1 respectively and hence the number is 561

Answer 2

"The three digit number is 642.

Given:

The sum of the “three digit number” is 12, if the “number is diminished” by 396.

To find:

The number

Solution:

Let the 3 digit number be a - d, a, a + d

Then it is given that it's sum is 12

(a-d)+(a)+(a+d)=12

a-d+a+a+d=12

3a = 12

$a=\frac{12}{3}$

a = 4.

Now if the digits are reversed,

100(a + d) + 10a + (a - d) = 100(a - d) + 10a + (a + d) - 396

Putting the value of a = 4 the equation will be

400 + 100d + 40 + 4 - d = 400 - 100d + 40 + 4 + d - 396

99d = -99d - 396

99d + 99d = -396

198d = -396

$d=\frac { -396 }{ 198 }$

d = -2

With a = 4 and d = -2

The number is (a – d), (a), (a + d)

[4 - ( -2)], (4), [(4 + (-2)]

The three digit number is 642. "