Let's break down the problem step-by-step.

Problem Analysis

Let $A_0$ and $B_0$ be the amounts of money A and B started with, respectively.

Step 1: First Game

• A loses the first game, so A must double B's money.
• Initially, A has $A_0$ and B has $B_0$.
• After the first game:
  • A gives B $B_0$ amount of money, so A’s new amount is $A_0 - B_0$.
  • B receives this money, so B’s new amount is $B_0 + B_0 = 2B_0$.

Now, the amounts are:

• A: $A_0 - B_0$
• B: $2B_0$

Step 2: Second Game

• B loses the second game, so B must double A's money.
• After the second game:
  • B gives A $A_0 - B_0$ amount of money, so B’s new amount is $2B_0 - (A_0 - B_0)$.
  • A receives this money, so A’s new amount is $(A_0 - B_0) + (A_0 - B_0) = 2(A_0 - B_0)$.

Now, the amounts are:

• A: $2(A_0 - B_0)$
• B: $3B_0 - A_0$

Step 3: Given Condition

We are told that after these two games, both A and B have Rs 120.

So, we have the equations: $2(A_0 - B_0) = 120 \quad \text{(1)}$ $3B_0 - A_0 = 120 \quad \text{(2)}$

Step 4: Solve the Equations

From equation (1): $A_0 - B_0 = 60 \quad \Rightarrow \quad A_0 = B_0 + 60 \quad \text{(3)}$

Substitute equation (3) into equation (2