Question : The ratio of the investments of A and B in a business is 7 : 5, and the ratio of their profits at the end of a year is 2 : 5. If A invested the money for 6 months, then for how much time (in months) has B invested his money?
Option 1: 12
Option 2: 21
Option 3: 24
Option 4: 18
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Correct Answer: 21
Solution :
Given: The investments of A and B in a business = 7 : 5
Profits at the end of a year = 2 : 5
Let the time of investment of B is $x$ months
The ratio of time of investment of A and B = $6 : x$
According to the question,
$\frac{\text{A's investment × A's time}}{\text{B's investment × B's time}} = \frac{\text{A's profit}}{\text{B's profit}}$
⇒ $\frac{7\times6}{5 \times x}=\frac{2}{5}$
⇒ $\frac{42}{5x}=\frac{2}{5}$
⇒ $42=2x$
⇒ $x=21$
Hence, the correct answer is 21.
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