A sum of Rs. 2,489 is divided among A, B and C. If Rs. 12, Rs. 12 and Rs. 5 are subtracted from the shares of A, B and C respectively, then their resulting shares are in the ratio 5 : 3 : 4. What is the new share of C (that is, C's share after the deduction)?

Introduction / Context:
This question is a ratio and distribution problem with a twist. The total amount is divided among three people A, B and C, but the ratio given applies not to their original shares but to the reduced amounts after specific deductions. We must reconstruct the original shares and then find the new share of C after the deduction of Rs. 5.

Given Data / Assumptions:

• Total amount divided among A, B and C is Rs. 2,489.
• If Rs. 12 is subtracted from A's share, Rs. 12 from B's share and Rs. 5 from C's share, the resulting amounts are in the ratio 5 : 3 : 4.
• We are asked to find C's new share, which is C's amount after the deduction of Rs. 5.

Concept / Approach:
Let the reduced shares of A, B and C be 5k, 3k and 4k respectively. These are the amounts after the subtractions. Then we can express the original shares in terms of k and sum them up to match the given total of Rs. 2,489. From there, we solve for k and compute C's reduced share directly. This is a common technique in ratio problems involving increases or decreases.

Step-by-Step Solution:
Step 1: Let A's reduced share be 5k, B's reduced share be 3k and C's reduced share be 4k.Step 2: A's original share = 5k + 12, because Rs. 12 was subtracted to get 5k.Step 3: B's original share = 3k + 12.Step 4: C's original share = 4k + 5.Step 5: The sum of original shares is (5k + 12) + (3k + 12) + (4k + 5) = 12k + 29.Step 6: This sum equals the given total amount, so 12k + 29 = 2,489.Step 7: Subtract 29 from both sides: 12k = 2,489 - 29 = 2,460.Step 8: Solve for k: k = 2,460 / 12 = 205.Step 9: C's reduced share is 4k = 4 * 205 = Rs. 820.

Verification / Alternative check:
Compute the original shares using k = 205. A's original share = 5 * 205 + 12 = 1,037. B's original share = 3 * 205 + 12 = 627. C's original share = 4 * 205 + 5 = 825. Sum is 1,037 + 627 + 825 = Rs. 2,489, which matches the given total. After subtracting 12, 12 and 5, the shares become 1,025, 615 and 820. The ratio 1,025 : 615 : 820 simplifies to 5 : 3 : 4, confirming the correctness of the calculation.

Why Other Options Are Wrong:
Values such as 750, 1,060 and 1,475 do not fit either the derived value of 4k or the total sum when you reconstruct the original shares. Using any of these would break the 5 : 3 : 4 ratio or the total of Rs. 2,489. 'None of these' is not correct because Rs. 820 is exactly the reduced share of C derived from the given conditions.

Common Pitfalls:
One common mistake is to directly apply the ratio 5 : 3 : 4 to the total amount 2,489 without accounting for the subtractions. Another is to mistakenly interpret 5k, 3k and 4k as the original shares instead of the reduced ones. Always carefully note whether the ratio applies before or after an adjustment to the amounts.

Final Answer:
The new share of C after the deduction is Rs. 820.