Two numbers are in a ratio of 1:4 and their sum is 50. What is the smaller number?

Let us assume the common ratio to be = x

Then

(1 * x) + (4 * x) = 50

x + 4x = 50

5x = 50

x = 50/5

= 10

So from the above deduction, we get the common ratio to be equal to 10

Then

The smallest number = 1 * x

= 1 * 10

= 10