Question

A 2-digit number has 5 for its units digit and the sum of digits is 1/5 of the number itself.find the number.

Answer 1

Given the two digit number (10x+y), where y = 5

And also given, x+y = (1/5) (10x+5)

solving for x,

(x+5)5=10x+5

5x+25 = 10x+5

or x=4

the required number is 45.

Answer 2

The number is 45.

Let the unit's digit be 'y' and the one's digit be 'x'.

So, the two digit number formed is (10x + y).

Given, unit's digit is 5, so y =5

The number formed is (10x + 5)

Sum of the digits in the number = (x + y) = (x + 5)                 [As y = 5]

Given that the sum of the digits = 1/5 × Number itself.

So,

(x + 5) = (1/5) × (10x + 5)

⇒ 5(x + 5) = 10x + 5

⇒ 5x + 25 = 10x + 5

⇒ 5x = 20

⇒ x = 20/5 = 4

And y = 5

Thus number is (10x + 5) = (10×4 + 5) = 45