To solve this problem, we first need to understand what the question is asking us to do. We are given a number, and we are told that if we take its fifth part and add 5 to it, we get the same result as if we take its fourth part and subtract 5 from it. In other words, we need to find a number that satisfies the equation:

5x/5 + 5 = 4x/4 - 5

where "x" is the unknown number we are trying to find.


To solve for "x", we first need to simplify the equation. We can do this by cross-multiplying to get rid of the fractions:

4(5x/5 + 5) = 5(4x/4 - 5)

Simplifying this equation, we get:

4x + 20 = 5x - 25


Now we can solve for "x" by isolating it on one side of the equation. We can do this by subtracting 4x from both sides and adding 25 to both sides:

4x + 20 - 4x = 5x - 25 - 4x + 25

Simplifying this equation, we get:

20 = x

Therefore, the number we are looking for is 20.


In conclusion, we have found that the number whose fifth part increased by 5 is equal to its fourth part diminished by 5 is 20. We arrived at this answer by simplifying the equation and solving for "x".