Rs 490 is divided among A, B and C such that the share of A is half of the share of B and three times the share of C. What is the share of C in rupees?

Introduction / Context:
This question is a basic application of linear relationships between three shares. One person share is linked to the second and third shares through stated multiples. Using these relationships and the total sum, we can set up equations and solve for each individual share. The final objective is to find how much C receives from the total Rs 490.

Given Data / Assumptions:
Total amount to be distributed is Rs 490. Share of A is half of share of B. Share of A is three times share of C. We need to find share of C.

Concept / Approach:
We can let one share be a variable and express the others in terms of that variable using the relationships given. Then we use the fact that the sum of all three shares equals Rs 490. This leads to a simple equation which we solve to find the base share. Once A share is known, we compute C share using the relation that A is three times C. This approach avoids guesswork and provides a clear algebraic route to the answer.

Step-by-Step Solution:
Step 1: Let share of A be A rupees, share of B be B rupees and share of C be C rupees. Step 2: A is half of B, so A = B / 2, which implies B = 2A. Step 3: A is three times C, so A = 3C, which implies C = A / 3. Step 4: Total amount is A + B + C = 490. Step 5: Substitute B = 2A and C = A / 3 into the total: A + 2A + A / 3 = 490. Step 6: Combine like terms: A + 2A = 3A, so 3A + A / 3 = 490. Step 7: Express in terms of a single denominator: 3A = 9A / 3, so 9A / 3 + A / 3 = 10A / 3. Step 8: Therefore 10A / 3 = 490. Step 9: Multiply both sides by 3 to get 10A = 1470. Step 10: So A = 1470 / 10 = Rs 147. Step 11: C = A / 3 = 147 / 3 = Rs 49.

Verification / Alternative check:
Using A = 147 and C = 49, B = 2A = 294. The total sum is A + B + C = 147 + 294 + 49 = 490, which matches the given total amount. Also, A is half of B because 147 is half of 294 and A is three times C because 147 = 3 * 49. All conditions are satisfied, so the calculation for C share is correct.

Why Other Options Are Wrong:
Rs 147 is the share of A, not of C, and would make A and C equal which violates A = 3C. Rs 294 is the share of B and is twice A, not one third of A. Rs 245 would make the sum of shares exceed 490 or break the given relationships. Only Rs 49 fits every constraint and correctly represents C share.

Common Pitfalls:
Some learners accidentally treat statements like half and three times in the reverse direction, for example assuming B is half of A instead of A being half of B. Another mistake is to forget to include all three shares when forming the total. Carefully translating the language of the problem into equations and checking each relationship after solving helps avoid these issues.

Final Answer:
The share of C from the Rs 490 is Rs 49.