Question : A man spends $7\frac{1}{2}$% of his money, and after spending 75% of the remaining, he has Rs. 370 left. How much money did he initially have?
Option 1: Rs. 1200
Option 2: Rs. 1600
Option 3: Rs. 1500
Option 4: Rs. 1400
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Correct Answer: Rs. 1600
Solution : Given: A man spends $7\frac{1}{2}$% of his money and after spending 75% of the remaining has Rs. 370 left. Now, $7\frac{1}{2}$% = $\frac{3}{40}$ and $75$% = $\frac{3}{4}$ Let the income of the man be Rs. $x$. At first, the man spent $\frac{3}{40}$ of $x$ money. So, the money left = $(1 - \frac{3}{40})x = (\frac{37}{40})x$, and then he spent $\frac{3}{4}$th of the remaining money. So, the left amount of money will be $(1 - \frac{3}{4}) = \frac{1}{4}$th of the remaining money. According to the given information, $x × (\frac{37}{40}) × (\frac{1}{4}) = 370$ ⇒ $x = 370 × (\frac{4}{1}) × (\frac{40}{37}$) So, $x = 1600$ Hence, the correct answer is Rs. 1600.
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