Question

At the start of a game of cards, J and B together had four times as much money as T, while T and B together had three times as much as J. At the end of the evening, J and B together had three times as much money as T, while T and B together had twice as much as J. B lost Rs. 200.

What amount did B start with?

• A. Rs. 575
• B. Rs. 375
• C. Rs. 825
• D. Rs. 275

Hint:

Express B's beginning and ending share in terms of T1 using the given ratios, then use B's Rs. 200 loss to solve for T1.

Answer 1

The Correct Option is C

Step 1: Build the beginning and ending shares in terms of x.
Using total \(=60x\): beginning shares are \(T1=12x\), \(J1=15x\), \(B1=33x\) (from \(J+B=4T\), \(T+B=3J\)). Ending shares are \(T2=15x\), \(J2=20x\), \(B2=25x\) (from \(J2+B2=3T2\), \(T2+B2=2J2\)).

Step 2: Use B's loss to pin down x.
B's change is \(B1 - B2 = 33x - 25x = 8x\), and this is a loss of Rs. 200, so \(8x = 200\), giving \(x = 25\).

Step 3: Compute B's starting amount.
\(B1 = 33x = 33 \times 25 = Rs.\ 825\).

Step 4: Sanity check the full picture.
T1 = 12(25) = 300, J1 = 15(25) = 375, total = 300+375+825 = 1500 = 60(25), consistent. At the end, T2=375, J2=500, B2=625, total still 1500, and B2 is indeed 200 less than B1 (825-625=200).

Step 5: Rule out the other options.
Rs. 375 is J's starting amount, not B's. Rs. 575 and Rs. 275 do not satisfy \(8x=200\) with \(x=25\).

Final Answer:
B started the game with Rs. 825. \[ \boxed{Rs.\ 825} \]