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  1. The sum of the present ages of Ato Moges and his daughter is 50 years. In 5 years' time Ato
    Moges will be 3 times as old as his daughter. How old is his daughter?
    A. 10 years
    B. 12 years
    C. 8 years D. 5 years

Verified Answer :

GinnyAnswer

To solve this problem, let's denote the current age of Ato Moges as \(\( M \)\) and the current age of his daughter as \(\( D \)\).

First, we are given that the sum of their current ages is 50 years:
\(\[ M + D = 50 \]\)

Next, we are also given that in 5 years, Ato Moges will be 3 times as old as his daughter:
\(\[ M + 5 = 3 \times (D + 5) \]\)

Now we have two equations:
1. \(\( M + D = 50 \)\)
2. \(\( M + 5 = 3 \times (D + 5) \)\)

Let's start by solving the second equation for \(\( M \)\):
\(\[ M + 5 = 3(D + 5) \]\)
\(\[ M + 5 = 3D + 15 \]\)
\(\[ M = 3D + 10 \]\)

Now we substitute \(\( M \)\) from this equation into the first equation:
\(\[ (3D + 10) + D = 50 \]\)
\(\[ 4D + 10 = 50 \]\)
\(\[ 4D = 40 \]\)
\(\[ D = 10 \]\)

Therefore, Ato Moges' daughter is currently 10 years old.

So, the correct answer is:
A. 10 years

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