Capital exchange puzzle: One says, “Give me one hundred, friend! I will then be twice as rich as you.” The other replies, “If you give me ten, I shall be six times as rich as you.” Find each person’s capital (in ₹).

Introduction / Context:
This is a classic two-variable word problem involving linear equations formed from statements about how capitals change after giving fixed amounts. Translate each sentence carefully into an equation and solve simultaneously for the two unknown capitals.

Given Data / Assumptions:

• Let A and B be the current capitals (in ₹) of the first and second persons respectively.
• “Give me 100; I then become twice as rich as you”: A + 100 = 2(B − 100).
• “If you give me 10; I shall be six times as rich as you”: B + 10 = 6(A − 10).

Concept / Approach:
Each statement yields a linear relation. Solve the two equations for A and B using substitution or elimination. Finally, check both conditions to ensure internal consistency before selecting the option.

Step-by-Step Solution:

Verification / Alternative check:
Check first claim: A + 100 = 140; B − 100 = 70; indeed 140 = 2*70. Second claim: B + 10 = 180; A − 10 = 30; 180 = 6*30. Both checks pass.

Why Other Options Are Wrong:
Other pairs do not satisfy both transformed equations simultaneously when verified; “Cannot be determined” is incorrect because the system is consistent and solvable uniquely.

Common Pitfalls:
Reversing who gives whom or sign errors when moving constants across the equals sign are common sources of mistakes in such puzzles.

Final Answer:
₹ 40 and ₹ 170