To solve this problem, let's denote the current age of Ato Moges as [tex]\( M \)[/tex] and the current age of his daughter as [tex]\( D \)[/tex].
First, we are given that the sum of their current ages is 50 years:
[tex]\[ M + D = 50 \][/tex]
Next, we are also given that in 5 years, Ato Moges will be 3 times as old as his daughter:
[tex]\[ M + 5 = 3 \times (D + 5) \][/tex]
Now we have two equations:
1. [tex]\( M + D = 50 \)[/tex]
2. [tex]\( M + 5 = 3 \times (D + 5) \)[/tex]
Let's start by solving the second equation for [tex]\( M \)[/tex]:
[tex]\[ M + 5 = 3(D + 5) \][/tex]
[tex]\[ M + 5 = 3D + 15 \][/tex]
[tex]\[ M = 3D + 10 \][/tex]
Now we substitute [tex]\( M \)[/tex] from this equation into the first equation:
[tex]\[ (3D + 10) + D = 50 \][/tex]
[tex]\[ 4D + 10 = 50 \][/tex]
[tex]\[ 4D = 40 \][/tex]
[tex]\[ D = 10 \][/tex]
Therefore, Ato Moges' daughter is currently 10 years old.
So, the correct answer is:
A. 10 years
