Rs. 2430 is divided among A, B, and C. If their shares are reduced by Rs. 5, Rs. 10, and Rs. 15 respectively, the resulting amounts are in the ratio 3 : 4 : 5. What is A’s original share?

Introduction / Context:
Adjusted ratios often point to “let the new amounts be 3k, 4k, 5k,” then add back the adjustments to retrieve the original shares. The sum of original shares must equal the given total.

Given Data / Assumptions:

• A − 5 : B − 10 : C − 15 = 3 : 4 : 5
• A + B + C = 2430

Concept / Approach:
Let A − 5 = 3k, B − 10 = 4k, C − 15 = 5k. Then A = 3k + 5, B = 4k + 10, C = 5k + 15. Summing and equating to 2430 yields k; substitute back to get A.

Step-by-Step Solution:
A = 3k + 5, B = 4k + 10, C = 5k + 15A + B + C = (3k + 5) + (4k + 10) + (5k + 15) = 12k + 30 = 243012k = 2400 ⇒ k = 200A = 3k + 5 = 600 + 5 = 605

Verification / Alternative check:
New amounts: A − 5 = 600, B − 10 = 810, C − 15 = 985. Their ratio is 600 : 810 : 985 = 3 : 4 : 5 after simplifying by a common factor of 200 for the first two and checking the third consistency (constructed via 5k).

Why Other Options Are Wrong:
Other choices do not fit the 3k, 4k, 5k structure when rechecked with the original conditions.

Common Pitfalls:
Forgetting to add back the reductions or summing the reduced amounts to 2430 (which would be incorrect).

Final Answer:
Rs. 605