X and Y are partners in a business. X contributed $$\frac{1}{3}$$ of the capital for 9 months and Y received $$\frac{2}{5}$$ of the profit. For how long was Y's money used in the business ?
A. 2 months
B. 3 months
C. 4 months
D. 5 months
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & {\text{Let the total profit be Rs}}{\text{.}}\,z \cr & {\text{Then,}} \cr & {\text{Y's share}} = {\text{Rs}}{\text{.}}\,\frac{{2z}}{5} \cr & {\text{X's share}} = {\text{Rs}}{\text{.}}\left( {z - \frac{{2z}}{5}} \right) \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}.\,\frac{{3z}}{5} \cr & \therefore {\text{X}}:{\text{Y}} \cr & = \frac{{3z}}{5}:\frac{{2z}}{5} \cr & = 3:2 \cr} $$Let the total capital be Rs. x and
Suppose Y's money was used for y months
Then,
$$\eqalign{ & \Rightarrow \frac{{\frac{1}{3}x \times 9}}{{\frac{2}{3}x \times y}} = \frac{3}{2} \cr & \Rightarrow 18x = 6xy \cr & \Rightarrow y = 3 \cr} $$
Hence, Y's money was used for 3 months.
Related Questions on Partnership
A. 5 : 7 : 8
B. 20 : 49 : 64
C. 38 : 28 : 21
D. None of these
A. Rs. 40000
B. Rs. 50000
C. Rs. 60000
D. Rs. 70000
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