Question : A person loses 75% of his money in the first bet, 75% of the remaining in the second bet and 75% of the remaining in the third bet and returns home with only Rs. 2. His initial money was:
Option 1: Rs. 64
Option 2: Rs. 128
Option 3: Rs. 256
Option 4: Rs. 512
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Correct Answer: Rs. 128
Solution :
Let the person have Rs. $x$ initially.
He loses $75$% of his money up to the third bet and returns home with Rs. 2.
According to the question,
$x×\frac{100–75}{100}×\frac{100–75}{100}×\frac{100–75}{100}=2$
$⇒ x×\frac{1}{4}×\frac{1}{4}×\frac{1}{4}=2$
$⇒ x=128$
Hence, the correct answer is Rs. 128.
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