Robin says, "If Jai gives me ₹ 40, he will have half as much as Atul, but if Atul gives me ₹ 40, then the three of us will have the same amount." What is the total amount of money that Robin, Jai and Atul have between them?

## Concept & Logic This requires setting up linear equations based on conditional monetary transfers. Finding a common baseline variable from the "everyone has the same amount" condition makes solving it much faster. Let the initial amounts of Robin, Jai, and Atul be $r$, $j$, and $a$ respectively. ## Step-by-Step Solution * **Analyze Condition 2 (The Equalizer):** * "If Atul gives Robin ₹ 40, then the three of us will have the same amount." * Let this final equal amount be $x$. * Robin receives 40: $r + 40 = x \Rightarrow r = x - 40$ * Jai's amount didn't change in this scenario: $j = x$ * Atul gives 40: $a - 40 = x \Rightarrow a = x + 40$ * Now all variables are expressed in terms of $x$. The total money is $r + j + a = (x - 40) + x + (x + 40) = 3x$. * **Analyze Condition 1:** * "If Jai gives Robin ₹ 40, Jai will have half as much as Atul." * Jai's new amount = $j - 40 = x - 40$ * Atul's amount remains $a = x + 40$ (in this specific conditional scenario). * Set up the equation: $$ x - 40 = \frac{1}{2}(x + 40) $$ $$ 2(x - 40) = x + 40 $$ $$ 2x - 80 = x + 40 $$ $$ x = 120 $$ * **Calculate Total Amount:** * Total Amount = $3x = 3 \times 120 = 360$. ## Exam Strategy & Shortcut Use the "same amount" clue to bypass three-variable systems. Since moving 40 from Atul to Robin equalizes everyone without involving Jai, it immediately tells you Jai is already holding the average amount ($x$). Total money is always $3 \times \text{Average}$, so Total = $3 \times \text{Jai}$. From the first statement: $(\text{Jai} - 40) = \frac{1}{2}(\text{Jai} + 40)$ because Atul must be $\text{Jai} + 40$ to reach the average when he loses 40. Solving gives $\text{Jai} = 120$. Total = $360$. ## Common Pitfall Creating three separate variables $r$, $j$, $a$ and trying to solve a messy $3 \times 3$ system of equations via substitution. This eats up valuable time and increases calculation errors. Always look for a pivot variable (like Jai in this case) to unify the terms. ## Final Answer Therefore, the correct answer is **₹ 360**.