Two scenarios, two equations (money transfer): Ram and Mohan have some money. If Ram gives ₹30 to Mohan, Mohan then has twice as much as Ram has left. If instead Mohan gives ₹10 to Ram, Ram then has three times as much as Mohan has left. How much money does each have?

Introduction / Context:
This is a pair of linear equations derived from two hypothetical money transfers. Define variables for Ram's and Mohan's current amounts, translate each scenario into an equation, and solve simultaneously.

Given Data / Assumptions:

• Let R = Ram's money, M = Mohan's money.
• Scenario 1: M + 30 = 2(R − 30).
• Scenario 2: R + 10 = 3(M − 10).

Concept / Approach:
Each scenario produces a linear relationship between R and M. Solve the system by substitution or elimination to find integer solutions matching the options.

Step-by-Step Solution:

Verification / Alternative check:
Check Scenario 1: Ram gives 30 ⇒ R − 30 = 32; Mohan gets 30 ⇒ M + 30 = 64 = 2*32. Check Scenario 2: Mohan gives 10 ⇒ M − 10 = 24; Ram gets 10 ⇒ R + 10 = 72 = 3*24. Both conditions satisfied.

Why Other Options Are Wrong:

• ₹6,₹2 or ₹43,₹26 or ₹170,₹124: Do not satisfy both equations simultaneously when tested.

Common Pitfalls:
Sign mistakes when moving terms across the equals sign, or mixing up which person gives/receives money in each scenario.

Final Answer: