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A man lost half of his initial amount in the gambling after playing 3 rounds. The rule of gambling is that if he wins then he will  receive Rs. 100, but he has to give 50% of the total amount after each round. Luckily he won all the three rounds. The initial amount with which he had started the gambling was:
  • a)
    500/3
  • b)
    700/3
  • c)
    300
  • d)
    600
Correct answer is option 'B'. Can you explain this answer?
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A man lost half of his initial amount in the gambling after playing 3 ...
Let the initial amount be x (with gambler), then
 
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A man lost half of his initial amount in the gambling after playing 3 ...
Solution:
Let’s assume the initial amount as x.

After the first round, he lost 50% of the amount, which means he was left with x/2.

After the second round, he again lost 50% of the remaining amount, which means he was left with x/4.

After the third round, he again lost 50% of the remaining amount, which means he was left with x/8.

But he won all the three rounds, which means he received Rs. 100 after each round.

Therefore, the final amount he has is x/8 + 100 + 50% (x/8 + 100) = x/8 + 100 + x/16 + 50

Simplifying the above equation, we get:

x/2 = x/8 + 100 + x/16 + 50

Multiplying the above equation by 16, we get:

8x = 2x + 1600 + x + 800

Simplifying the above equation, we get:

5x = 2400

x = 480

Hence, the initial amount with which he had started the gambling was 480.

Therefore, option B is the correct answer.
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A man lost half of his initial amount in the gambling after playing 3 ...
Let the initial amount be x (with gambler), then
 
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A man lost half of his initial amount in the gambling after playing 3 rounds. The rule of gambling is that if he wins then he will receive Rs. 100, but he has to give 50% of the total amount after each round. Luckily he won all the three rounds. The initial amount with which he had started the gambling was:a)500/3b)700/3c)300d)600Correct answer is option 'B'. Can you explain this answer?
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