| Aayush and Babloo are partners in a business. Aayush contributes \[\frac{1}{4}\]of the capital for 15 months and Babloo received \[\frac{2}{3}\]of the profit. How long Babloo's money was used? |
A) 10 months
B) 9 months
C) 11 months
D) 7 months
E) None of these
Correct Answer: A
Solution :
| Let the total capital be Rs. x and Babloo's money is used for y months. |
| Capital of Aayush \[=\frac{x}{4}\] |
| \[\therefore \]Capital of Babloo \[=\left( x-\frac{x}{4} \right)=\frac{3x}{4}\] |
| Ratio of investments of Aayush and Babloo |
| \[=\left( \frac{x}{4}\times 15 \right):\left( \frac{3x}{4}\times y \right)=\frac{15}{4}:\frac{3y}{4}=5:y\] |
| Ratio of profits of Aayush and Babloo\[=\frac{1}{3}:\frac{2}{3}=1:2\] |
| \[\therefore \] \[\frac{5}{y}=\frac{1}{2}\]\[\Rightarrow \]\[y=10\] |
| Hence, Babloo's money was used for 10 months. |
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