1. **Stating the problem:** We have two groups of people: Amoako, Ben, Charles and Blay, Daniel, Evans. Each group receives money in the ratio 2:5:3. 2. **Given:** - Amount distributed among Amoako, Ben, Charles is in ratio $2:5:3$. - Amount distributed among Blay, Daniel, Evans is also in ratio $2:5:3$. - The total amount for Amoako, Ben, Charles is $\frac{2}{5}$ of the total amount for Blay, Daniel, Evans. 3. **Let:** - Total amount for Amoako, Ben, Charles be $A$. - Total amount for Blay, Daniel, Evans be $B$. 4. **Expressing amounts:** - Amoako's share = $2x$, - Ben's share = $5x$, - Charles' share = $3x$, where $x$ is a common multiplier for the first group. - Blay's share = $2y$, - Daniel's share = $5y$, - Evans' share = $3y$, where $y$ is a common multiplier for the second group. 5. **Using the given relation:** $$A = 2x + 5x + 3x = 10x$$ $$B = 2y + 5y + 3y = 10y$$ Given $A = \frac{2}{5} B$, so: $$10x = \frac{2}{5} \times 10y$$ $$10x = 4y$$ 6. **Solving for $x$ in terms of $y$:** $$x = \frac{4y}{10} = \frac{2y}{5}$$ 7. **Find the ratio of Amoako, Charles, and Evans:** - Amoako's share = $2x = 2 \times \frac{2y}{5} = \frac{4y}{5}$ - Charles' share = $3x = 3 \times \frac{2y}{5} = \frac{6y}{5}$ - Evans' share = $3y$ 8. **Write the ratio:** $$\frac{4y}{5} : \frac{6y}{5} : 3y$$ 9. **Cancel $y$ and multiply all terms by 5 to clear denominators:** $$4 : 6 : 15$$ 10. **Simplify the ratio by dividing by 1 (no common factor other than 1):** $$4 : 6 : 15$$ **Final answer:** The ratio in which the amount is distributed among Amoako, Charles, and Evans is $4:6:15$.