A and B started a business in partnership by investing in the ratio of 7 : 9. After 3 months A withdraw $$\frac{2}{3}$$ of its investment and after 4 months from the beginning B withdraw $$33\frac{1}{3}$$ % of its investment. If a total earned profit is Rs. 10201 at the end of 9 months, find the share of each in profit ? Options: A . &nbspRs. 3535, Rs. 6666 B . &nbspRs. 3055, Rs. 5555 C . &nbspRs. 4503, Rs. 1345 D . &nbspRs. 3545, Rs. 3333

Answer: Option A Note : In such type of question we can assume ratio as per our need to avoid fraction Capital → A7 × 3 : B9 × 3 New Ratio, → A21x : B27x Total capital invested by A in 9 months $$\eqalign{ & = 21x \times 3 + 7x \times 6 \cr & = 105x \cr} $$ Total capital of B invested in 9 months $$\eqalign{ & = 27x \times 4 + 18x \times 5 \cr & = 198x \cr} $$ $$\eqalign{ & {\text{According to the question,}} \cr & \left( {105x + 198x} \right) = {\text{Rs}}{\text{. 10201}} \cr & 303x = {\text{Rs}}{\text{. 10201}} \cr & x = \frac{{10201}}{{303}} \cr & {\text{Hence,}} \cr & {\text{Share of A}} = 105 \times \frac{{10201}}{{303}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,3535 \cr & {\text{Share of B}} = 198 \times \frac{{10201}}{{303}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {\text{Rs}}{\text{.}}\,{\text{6666}} \cr} $$