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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