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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