To determine which of the given options is the maximum share of the 20,000 Birr divided among three persons in the ratio 5:2:3, we need to follow these steps:
1. Understand the ratio:
The three persons are sharing the amount of 20,000 Birr in the ratio of 5:2:3.
2. Sum of the ratio terms:
Add up the parts of the ratio:
[tex]\[
5 + 2 + 3 = 10
\][/tex]
3. Determine the share for each person:
Correspond each part of the ratio to a portion of the total amount:
- For the first person (ratio part = 5):
[tex]\[
\text{Share of first person} = \frac{5}{10} \times 20,000 = 10,000 \text{ Birr}
\][/tex]
- For the second person (ratio part = 2):
[tex]\[
\text{Share of second person} = \frac{2}{10} \times 20,000 = 4,000 \text{ Birr}
\][/tex]
- For the third person (ratio part = 3):
[tex]\[
\text{Share of third person} = \frac{3}{10} \times 20,000 = 6,000 \text{ Birr}
\][/tex]
4. Identify the maximum share:
Compare the shares calculated:
[tex]\[
\text{Shares are 10,000 Birr, 4,000 Birr, and 6,000 Birr}
\][/tex]
The largest amount among these shares is 10,000 Birr.
Thus, the maximum share is:
[tex]\[
\boxed{\text{10,000 Birr}}
\][/tex]
Answer: B. 10,000 Birr
