Changing investments after a year adjusts the ratio: A, B, C initially invest in the ratio 3 : 5 : 7. After one year, C adds ₹ 3,37,600 and A withdraws ₹ 45,600. The new investment ratio becomes 24 : 59 : 167. Find A’s initial investment.

Introduction / Context:
This problem links an initial ratio to a later ratio after specific additions and withdrawals. Express the initial amounts with a single variable and transform them as described. Equate each transformed amount to the corresponding part of the new ratio to solve for the variable and hence the exact initial figure requested.

Given Data / Assumptions:

• Initial A : B : C = 3x : 5x : 7x.
• After 1 yr: A → 3x − 45,600; B → 5x; C → 7x + 3,37,600.
• New ratio = 24 : 59 : 167.

Concept / Approach:
Set 3x − 45,600 = 24k, 5x = 59k, 7x + 3,37,600 = 167k for some k. Solve from the cleanest equation 5x = 59k first, then substitute into the others to determine k and x consistently.

Step-by-Step Solution:

Verification / Alternative check:
Check with C: 7x + 3,37,600 = 3,30,400 + 3,37,600 = 6,68,000; and 167k = 167 * 4,000 = 6,68,000, consistent.

Why Other Options Are Wrong:
Other values do not satisfy all three new-ratio equations simultaneously after substitutions.

Common Pitfalls:
Solving only two of the three equations or using addition in the wrong direction (e.g., adding instead of subtracting for A).

Final Answer:
Rs. 1,41,600