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.

Question

Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: From Scenario 1: M + 30 = 2R − 60 ⇒ M = 2R − 90.From Scenario 2: R + 10 = 3M − 30 ⇒ R = 3M − 40.Substitute R into M = 2R − 90: M = 2(3M − 40) − 90 = 6M − 80 − 90 ⇒ −5M = −170 ⇒ M = 34.Then R = 3*34 − 40 = 102 − 40 = 62. 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: ₹62,₹34

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?

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