When Joni, Katrina, and Leah started their business, JKL Enterprises, each contributed an amount of money, in euros. The amounts...
GMAT Two Part Analysis : (TPA) Questions
When Joni, Katrina, and Leah started their business, JKL Enterprises, each contributed an amount of money, in euros. The amounts were in the ratio of \(3:5:8\), respectively, and the first-year profit of JKL Enterprises was split in the same ratio. Katrina's share of the first-year profit was €5,000.
Select for First-year profit and for Leah's share amounts in euros that are consistent with the given information and could be the first-year profit of JKL Enterprises and Leah's share of those profits, respectively. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Visual Representation
Let's create a simple ratio diagram to show the profit sharing:
Total Profit Split (3:5:8 ratio)
|---Joni---|---Katrina---|-------Leah-------|
3 parts 5 parts 8 parts
= €5,000 = ?
Total parts = \(3 + 5 + 8 = 16\) parts
Key Information
- Joni : Katrina : Leah = \(3 : 5 : 8\) (for both contributions and profit sharing)
- Katrina's profit share = €5,000
- We need to find: Total profit and Leah's share
Phase 2: Understanding the Question
Breaking Down the Relationships
Since Katrina gets 5 parts out of 16 total parts:
- Katrina's share = \(\frac{5}{16}\) of total profit = €5,000
This gives us the key equation:
\(\frac{5}{16} \times \text{Total Profit} = €5,000\)
Phase 3: Finding the Answer
Calculating Total Profit
From our equation: \(\frac{5}{16} \times \text{Total Profit} = €5,000\)
Solving for Total Profit:
Total Profit = \(€5,000 \times \frac{16}{5} = €5,000 \times 3.2 = €16,000\)
Calculating Leah's Share
Leah gets 8 parts out of 16 total parts:
Leah's share = \(\frac{8}{16} \times €16,000 = \frac{1}{2} \times €16,000 = €8,000\)
Verification
Let's check our answer:
- Joni's share = \(\frac{3}{16} \times €16,000 = €3,000\)
- Katrina's share = \(\frac{5}{16} \times €16,000 = €5,000\) ✓
- Leah's share = \(\frac{8}{16} \times €16,000 = €8,000\)
- Total = \(€3,000 + €5,000 + €8,000 = €16,000\) ✓
Phase 4: Solution
Final Answer:
- First-year profit: €16,000
- Leah's share: €8,000
Our answer satisfies all requirements: Katrina receives exactly €5,000 (which is \(\frac{5}{16}\) of €16,000), and the total splits perfectly in the \(3:5:8\) ratio.