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 ?
a) Rs. 3535, Rs. 6666
b) Rs. 3055, Rs. 5555
c) Rs. 4503, Rs. 1345
d) Rs. 3545, Rs. 3333

Answer: a
Explanation: Note :In such type of question we can assume ratio as per our need to avoid fraction

Capital →	A 7 × 3	:	B 9 × 3
New Ratio, →	A 21x	:	B 27x

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
$$\eqalign{ & = 27x \times 4 + 18x \times 5 \cr & = 198x \cr} $$
$$\eqalign{ & \left( {105x + 198x} \right) = {\text{Rs}}{\text{. 10201}} \cr & 303x = {\text{Rs}}{\text{. 10201}} \cr & x = \frac{{10201}}{{303}} \cr & {\text{Share of A}} = 105 \times \frac{{10201}}{{303}} = {\text{Rs}}{\text{.}}\,3535 \cr & {\text{Share of B}} = 198 \times \frac{{10201}}{{303}} = {\text{Rs}}{\text{.}}\,{\text{6666}} \cr} $$