Rs 11,550 has to be divided between X, Y & Z such that X gets 4/5 of what Y gets and Y gets 2/3 of what Z gets. How much more does Z get over X (in Rs)?
Explanation:
- We have Rs 11,550 to divide among X, Y, and Z.
- X gets 4/5 of what Y receives.
- Y gets 2/3 of what Z receives.
- Let's denote Z's share with Z. Then, Y gets \( \frac{2}{3}Z \).
- X receives \( \frac{4}{5} \times \frac{2}{3}Z = \frac{8}{15}Z \).
- The total becomes \( Z + \frac{2}{3}Z + \frac{8}{15}Z = 11,550 \).
- Simplifying, \( \frac{45 + 30 + 24}{45}Z = 11,550 \).
- \( \frac{99}{45}Z = 11,550 \) becomes \( Z = \frac{11,550 \times 45}{99} \).
- Calculating, \( Z = 5,250 \).
- X's amount: \( \frac{8}{15}Z = 2,800 \).
- Z gets \( 5,250 - 2,800 = 2,450 \) more than X.
- The correct answer is Option 3: 2450
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By: sunny bhonsle