M, N, and P together invest ₹ 50,000. M invests ₹ 4,000 more than N, and N invests ₹ 5,000 more than P. If the total profit is ₹ 70,000, what is M's share of the profit?

Introduction / Context:
When absolute differences among investments are given with a known total, solve for each capital first. Profit then divides proportional to those capitals (assuming equal time).

Given Data / Assumptions:

• Total capital = ₹ 50,000.
• Let P = x; N = x + 5,000; M = x + 9,000.
• Total profit = ₹ 70,000; time equal for all.

Concept / Approach:
Solve 3x + 14,000 = 50,000 to find x, then compute the ratio M : N : P and apply it to the profit.

Step-by-Step Solution:
3x + 14,000 = 50,000 ⇒ 3x = 36,000 ⇒ x = 12,000. P = 12,000; N = 17,000; M = 21,000. Ratio = 21,000 : 17,000 : 12,000. Total = 50,000; M's fraction = 21,000/50,000 = 0.42. M's share = 0.42 * 70,000 = ₹ 29,400.

Verification / Alternative check:
N's share would be 0.34 * 70,000 = ₹ 23,800 and P's share 0.24 * 70,000 = ₹ 16,800; totals match ₹ 70,000.

Why Other Options Are Wrong:
They do not reflect the 21:17:12 split derived from the constraints.

Common Pitfalls:
Misreading who invested more than whom, or assuming equal shares without using the capital differences.

Final Answer:
₹ 29,400