A total of Rs 10,200 is to be divided among three people A, B, and C so that A receives 2/3 of what B receives and B receives 1/4 of what C receives.\nHow many rupees more does C receive than A?

Introduction / Context:
This question is a classic ratio and proportion problem presented in words. The shares of three people A, B, and C are linked through fractional relationships rather than directly stated ratios. From these relationships and the total amount to be distributed, we must determine the individual shares and then compare two of them. Such problems frequently appear in partnership, division of income, and allocation topics in aptitude tests.

Given Data / Assumptions:

• Total amount to be divided among A, B, and C = Rs 10200.
• A receives 2/3 of what B receives.
• B receives 1/4 of what C receives, so C receives four times what B receives.
• We need to find how much more C receives than A.
• All amounts are non negative and the entire sum is distributed among A, B, and C.

Concept / Approach:
We translate the verbal fractional relationships into algebraic equations. By letting B share be a variable, we can express A and C shares in terms of that same variable. Then we use the equation A + B + C = 10200 to solve for the variable. Once we know B share, we can compute A and C shares and finally determine the difference C minus A. This method turns a word problem into a straightforward algebraic system.

Step-by-Step Solution:
Step 1: Let B share be x rupees. Step 2: A receives 2/3 of B share, so A share = (2 / 3) * x. Step 3: B receives 1/4 of what C receives, so C share = 4 * x. Step 4: Total amount distributed is A + B + C = 10200. Step 5: Substitute the expressions: (2 / 3) * x + x + 4 * x = 10200. Step 6: Combine like terms. First sum the coefficients of x: (2 / 3) + 1 + 4 = (2 / 3) + 5. Step 7: Write 5 as 15 / 3, so combined coefficient is (2 / 3) + (15 / 3) = 17 / 3. Step 8: Therefore (17 / 3) * x = 10200. Step 9: Solve for x: x = 10200 * 3 / 17 = 1800. Step 10: So B share = Rs 1800. Then A share = (2 / 3) * 1800 = Rs 1200, and C share = 4 * 1800 = Rs 7200. Step 11: Difference between C and A shares = 7200 - 1200 = Rs 6000.

Verification / Alternative check:
Check that the three shares add up to the total and respect the conditions. Sum A, B, and C shares: 1200 + 1800 + 7200 = 10200, which matches the total given. Also A receives 2/3 of B share since 2 / 3 of 1800 is 1200, and B receives 1/4 of C share since 1 / 4 of 7200 is 1800. Both conditions are satisfied exactly, so the algebraic solution is consistent and the difference of Rs 6000 between C and A is correct.

Why Other Options Are Wrong:
A difference of Rs 7200 would imply extremely unbalanced shares that would violate the given fractional relationships. A difference of Rs 1800 or Rs 1200 is too small and would not match the computed values from the equations. When the relationships and total are applied correctly, only a difference of Rs 6000 is possible, and the other values are incompatible with the constraints of the problem.

Common Pitfalls:
One common mistake is reversing the fraction relationship, for example interpreting “A gets 2/3 of what B gets” as the opposite or misreading “B gets 1/4 of what C gets” as C gets 1/4 of B. Another issue is trying to convert the word description directly into a ratio without carefully tracing who depends on whom. Introducing a variable for one person share and writing all other shares in terms of that variable is the safest and clearest method.

Final Answer:
C receives Rs 6000 more than A.