**Ques - A three digit number is such that this number itself is divisible by the sum of its digits.The sum of hundreds and unit digit is 6 while the sum of the tens and unit digit is 5. What is the ratio of unit and tens digits :**

**(a) 1 : 2**

**(b) 2 : 3**

**(c) 3 : 4**

**(d) 2 : 7**

**Solution -**

Let,

The three digits be,

x at hundred's place = 100x

y at tens place = 10y

and,

z at one's place = z

Since,

x + z = 6

and x can't be zero as it is a three-digit number.

So,

x and z can be : (x,z) = (1,5), (5,1), (2,4), (4,2), (3,3), (6,0)

Similarly,

y + z = 5

So,

y and z can be : (y,z) = (0,5), (5,0), (1,4), (4,1), (2,3), (3,2)

Since,

x, y and z are related ,

So,

If we take ,

x = 1, then z = 5

and,

when z = 5, then y = 0

Therefore,

The number becomes 105.

Similarly,

The other numbers are 214, 323, 432, 541 and 650.

So,

The number 432 is divisible by the sum of its digits.

4 + 3 + 2 = 9

also,

432/9 = 48.

Here,

Ten's digit = 3

and

Unit's digit = 2

__Therefore, __

**The ratio of units and tens digit = 2 : 3 .**

Hence,

The correct answer is option **(b) 2 : 3.**

Thank You