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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83% (03:41) correct
