Discussion

Question:

What BEST can be said about the amount of money that Ritesh had with him at the end of Round 8?

Explanation:

​​​​​​​Whenever a player has Rs. 10, it is already mentioned in the table. Their can be no other entry of Rs. 10.

Also, Highest and Lowest amounts of a player are also already mentioned.
E.g.: Pulak’s highest and lowest amount is Rs. 13 and Rs. 10 respectively in rounds 2, 8, 1 and 5. . Pulak cannot have Rs. 13 or more and Rs. 10 or less in any other round. Hence, the only amount Pulak can have at the end of any round is Rs. 11 or Rs. 12.

Allowed entries for
Pulak: 11 or 12
Qasim: 9 or 11
Ritesh: 5 or 6 or 7 or 8 or 9
Suresh: 9 or 11 or 12

Total amount at the end of any round should be same as the total amount initially i.e., Rs. 40.

Round 1: Amount with Pulak = 40 – (8 + 10 + 10) = Rs. 12
Ritesh and Suresh did not lose/gain, hence they paired up and decided not to play.
while, Qasim lost Rs. 2 to Pulak.

Round 2: Amount with Ritesh = 40 – (13 + 10 + 8) = Rs. 9
Pulak gained Rs. 1 while Ritesh lost Rs. 1. Hence, Pulak and Ritesh paired and bet Rs. 1.
while, Suresh paired up with Qasim for Rs. 2.

Round 5: Amount with Ritesh = 40 – (10 + 10 + 13) = Rs. 7

Round 7: Amount with Pulak and Suresh together = 40 – 12 – 4 = Rs. 24
Amount with Suresh and Pulak in Round 7 should be less than 13.
Only way this is possible is that both Pulak and Suresh have Rs. 12.

Round 8: Suresh loses Rs. 2. The only one who could gain Rs. 2 is Ritesh. Hence, Suresh paired with Ritesh and Pulak with Qasim.

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Round 4: Pulak and Qasim had same amount. This amount can only be Rs. 11.
Now Pulak and Qasim lose Rs. 1 each Round 5, hence Ritesh and Suresh must gain Rs. 1 in round 5.
⇒ Ritesh and Suresh had Rs. 1 less in round 4 than round 5.

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Round 3: Since Suresh paired with Qasim in round 2, he will pair with either Pulak or Ritesh in round 3.

If Suresh pairs with Ritesh, Ritesh will have Rs. 7 in round 3. Hence, Pulak  + Qasim will have Rs. 23. This is possible when Pulak has Rs. 12 and Qasim has Rs. 11.

But that would mean that only Qasim doesn’t bet in round 4 which is not possible.

∴ Suresh pairs with Pulak in round 3. Hence, Pulak will have Rs. 12 in round 3.
⇒ Qasim and Ritesh have together Rs. 18. This is possible when Qasim has Rs. and Ritesh has Rs. .

⇒ Pulak paired with Qasim in round 4 and Ritesh with Suresh.

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Round 6: Highest amount with Pulak, Qasim and Suresh in round 6 can be 12 + 11 + 12 = 35.
In that case Ritesh will have Rs. 5.

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Had the amount with Ritesh been Rs. 6 at the end of round 6. Other three will have a total of Rs. 34. In this case, we would not get proper arrangement for round 7.

Therefore, the final table is as follows:

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∴ The amount of money that Ritesh had with him at the end of Round 8 is Rs. 6.

Hence, option (d).

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