A sum of Rs. 4300 is distributed among three persons M, N and O. M receives 25% more than N and N receives 25% less than O. What is the share of O in the total amount?

Introduction / Context:
This question tests understanding of percentage relationships between different shares in a partnership type distribution. The key idea is to convert the percentage statements into algebraic expressions, form equations and then solve for the required share, in this case the share of O from a fixed total amount of Rs. 4300.

Given Data / Assumptions:

• Total amount distributed among M, N and O is Rs. 4300.
• M receives 25 percent more than N.
• N receives 25 percent less than O.
• We must find the amount received by O.
• All amounts are assumed to be positive real numbers.

Concept / Approach:
Percent increase and percent decrease can be converted into multiplicative factors. If someone receives 25 percent more than another, the multiplier is 1.25. If someone receives 25 percent less than another, the multiplier is 0.75. By letting one person's share be a variable, we can express all other shares in terms of that variable and then use the total sum to find exact numerical values.

Step-by-Step Solution:
Step 1: Let the share of N be N rupees. Step 2: M receives 25 percent more than N, so M = 1.25 * N = 5N / 4. Step 3: N receives 25 percent less than O, so N = 0.75 * O = 3O / 4. Step 4: From N = 3O / 4, express O in terms of N: O = 4N / 3. Step 5: Total amount is M + N + O = 4300. Step 6: Substitute M and O in terms of N: 5N / 4 + N + 4N / 3 = 4300. Step 7: Convert to a common denominator of 12: (15N + 12N + 16N) / 12 = 4300. Step 8: This gives 43N / 12 = 4300, so 43N = 4300 * 12 = 51600. Step 9: Therefore N = 51600 / 43 = 1200. Step 10: Now find O using O = 4N / 3 = 4 * 1200 / 3 = 1600.

Verification / Alternative check:
Using N = Rs. 1200 and O = Rs. 1600, M is 25 percent more than N. So M = 1.25 * 1200 = 1500. Check the total: M + N + O = 1500 + 1200 + 1600 = 4300, which matches the given sum. Also, N is 25 percent less than O because 1200 is 75 percent of 1600. This confirms that the calculations follow the percentage relationships correctly.

Why Other Options Are Wrong:
Rs. 1564 and Rs. 1632 do not give integer values for the other shares that add up to 4300 under the given percentage relationships.
Rs. 1714 also fails to satisfy both the 25 percent more and 25 percent less conditions when back calculated. Only Rs. 1600 keeps all three values consistent with the data and the total sum.

Common Pitfalls:
Learners sometimes confuse which person receives more or less and may invert the percentage multipliers. Another mistake is to mix up 25 percent less with dividing by 1.25 instead of multiplying by 0.75. It is safer to work with clear algebraic expressions and a common denominator when adding fractional expressions, as done here with denominator 12.

Final Answer:
The share of O in the total amount is Rs. 1600.