Question

A three digit no. is such that this no.itself is divisible by the sum of it's digit .The sum of hundreds and unit digits 6 while the sum of the tens and unit digit is 5.what is the ratio of unit and tens digits​

Answer 1

Given:

Three digit number such that it is divisible by the sum of its digits.

Sum of hundreds and units digit=6

Sum of tens and units digit=5

To Find:

The three digit number.

Solution:

Let the three digits be x at hundred's place,y at tens place and z at one's place.

Since, x + z=6

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

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

Similarly, y+z=5

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

Since, x and 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,$\dfrac{432}{9}$=48.)

Here, tens digit=3

and unit digit=5

Therefore, the ratio of units and tens digit=5:3.