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# A person who has Rs. 729 decides to play a game of betting. He wins

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Manager
Joined: 20 Aug 2017
Posts: 113
A person who has Rs. 729 decides to play a game of betting. He wins  [#permalink]

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27 Dec 2019, 04:47
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Difficulty:

55% (hard)

Question Stats:

21% (01:14) correct 79% (02:09) wrong based on 14 sessions

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Q. A person who has Rs. 729 decides to play a game of betting. He wins three times and loses three times, the wins and losses occurring in random order. The chance of a win is equal to the chance of a loss and he wins and loses by the same percentage of the amount by which he plays a particular round. The change in the final amount which he has with him with respect to the initial investment is Rs. 217. What is the wager (stake) as a fraction of the money remaining with him at the time of each betting?

A. $$\frac{1}{9}$$

B. $$\frac{1}{3}$$

C. $$\frac{2}{3}$$

D. $$\frac{3}{4}$$

E. Cannot be determined
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Joined: 19 Oct 2018
Posts: 1849
Location: India
Re: A person who has Rs. 729 decides to play a game of betting. He wins  [#permalink]

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27 Dec 2019, 11:28
Assume he bets x% of his stake every time

The amount of money he left with after 6 bets= $$729(1+\frac{x}{100})^3(1-\frac{x}{100})^3= 729(1-\frac{x^2}{10000})^3$$

As x is a positive number, $$729(1-\frac{x^2}{10000})^3$$ < 729

$$729(1-\frac{x^2}{10000})^3= 729-217=512$$

$$(1-\frac{x^2}{10000})^3= \frac{512}{729}$$

$$(1-\frac{x^2}{10000})= \frac{8}{9}$$

$$(\frac{x^2}{10000})=\frac{1}{9}$$

x=$$\frac{100}{3}$$ %

the wager (stake) as a fraction of the money remaining with him at the time of each betting=$$[1-(\frac{100}{300})]= \frac{2}{3}$$

uchihaitachi wrote:
Q. A person who has Rs. 729 decides to play a game of betting. He wins three times and loses three times, the wins and losses occurring in random order. The chance of a win is equal to the chance of a loss and he wins and loses by the same percentage of the amount by which he plays a particular round. The change in the final amount which he has with him with respect to the initial investment is Rs. 217. What is the wager (stake) as a fraction of the money remaining with him at the time of each betting?

A. $$\frac{1}{9}$$

B. $$\frac{1}{3}$$

C. $$\frac{2}{3}$$

D. $$\frac{3}{4}$$

E. Cannot be determined
Re: A person who has Rs. 729 decides to play a game of betting. He wins   [#permalink] 27 Dec 2019, 11:28