Question

The sum of the digits of a 2-digit number is 9. The number is 6 times the units digit. Find the number.​

Answer 1

Let, the ones digit of two digits number be, x.

Then, the tens digit of two digits number be, y.

So, the new number is, (10x + y).

It is Given that,

The sum of the digits is 9

So,

x + y = 9

x = 9 - y ....(i)

It is also given that,

The number is 6 times the units.

So,

10x + y = 6y ....(ii)

Now,

Subtracting equation (i) from (ii), we get,

10(9 - y) + y = 6y

90 - 10y + y = 6y

90 - 9y = 6y

15y = 90

y = 90 ÷ 15

y = 6

Therefore, We got the value of, y = 6.

On, putting the value of y = 6, in equation (i), we get,

x = 9 - y

x = 9 - 6

x = 3

Therefore, the number = 10x + y = 10(3) + 6 = 36