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Raj played three rounds of a game of chance. In each round

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Raj played three rounds of a game of chance. In each round [#permalink] New post 15 Nov 2012, 22:02
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Raj played three rounds of a game of chance. In each round he doubled the amount with himself and then gave a certain amount to his friend. The amount he gave his friend in each round was a quarter of his gain in the first round. If he had instead given to his friend in each round an amount equal to half of his gain in the first round he would have finally remained with rs 70 less than he actually did. Find the amount he started with in rs?

A. 80
B. 160
C. 40
D. 60
[Reveal] Spoiler: OA

Last edited by Bunuel on 16 Nov 2012, 03:02, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Raj played three rounds of a game of chance. In each round [#permalink] New post 16 Nov 2012, 03:02
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siddharthamaridi wrote:
Raj played three rounds of a game of chance. In each round he doubled the amount with himself and then gave a certain amount to his friend. The amount he gave his friend in each round was a quarter of his gain in the first round. If he had instead given to his friend in each round an amount equal to half of his gain in the first round he would have finally remained with rs 70 less than he actually did. Find the amount he started with in rs?

A. 80
B. 160
C. 40
D. 60


Say Raj has x rs.

Case when he gives to his friend in each round a quarter of his gain in the first round:
The amount he has after the first round: 2x-\frac{x}{4}=\frac{7x}{4};
The amount he has after the second round: 2*\frac{7x}{4}-\frac{x}{4}=\frac{13x}{4};
The amount he has after the third round: 2*\frac{13x}{4}-\frac{x}{4}=\frac{25x}{4}.

Case when he gives to his friend in each round half of his gain in the first round:
The amount he has after the first round: 2x-\frac{x}{2}=\frac{3x}{2};
The amount he has after the second round: 2*\frac{3x}{2}-\frac{x}{2}=\frac{5x}{2};
The amount he has after the third round: 2*\frac{5x}{2}-\frac{x}{2}=\frac{9x}{2}.

We are told that the difference is 70, thus \frac{25x}{4}-\frac{9x}{2}=70 --> x=40.

Answer: C.
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Re: Raj played three rounds of a game of chance. In each round [#permalink] New post 08 Dec 2012, 04:54
sometimes the wording of the questions confuse me

:cry:
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Re: Raj played three rounds of a game of chance. In each round [#permalink] New post 14 Aug 2013, 01:31
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Re: Raj played three rounds of a game of chance. In each round   [#permalink] 14 Aug 2013, 01:31
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