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A, B and C are partners in a business partnership. A invested Rs. 4000 for whole year. B invested Rs. 6000 initially but increased this investment up to Rs. 8000 at the end of 4 months, while C invested Rs. 8000 initially, but withdraw Rs. 2000 at the end of 9 months. At the end of year total earned profit is Rs. 16950, find their share of profit ?

a) Rs. 3600, Rs. 6600, Rs. 6750
b) Rs. 2000, Rs. 3050, Rs. 5400
c) Rs. 2450, Rs. 2460, Rs. 1456
d) None of these

Answer: a
Explanation: Total capital invested by A in 1 year
$$\eqalign{ & = 12 \times 4000 \cr & = {\text{Rs}}{\text{. 48000}} \cr} $$
Total capital invested by B in 1 year
$$\eqalign{ & = 4 \times 6000 + 8 \times 8000 \cr & = 24000 + 64000 \cr & = {\text{Rs}}{\text{.}}\,{\text{88000}} \cr} $$
Total capital invested by C in 1 year
$$\eqalign{ & = 9 \times 8000 + 3 \times 6000 \cr & = 72000 + 18000 \cr & = {\text{Rs}}{\text{. 90000}} \cr} $$
    A     :     B     :     C  
Capital   48000 : 88000 : 90000
  24 : 44 : 45

$$\left( {24 + 44 + 45} \right){\text{units}}$$     = $${\text{Rs}}{\text{.}}\,{\text{16950}}$$
$$\eqalign{ & {\text{113 units}} = {\text{Rs}}{\text{. 16950}} \cr & 1{\text{ unit}} = \frac{{16950}}{{113}}{\text{ = Rs}}{\text{. 150}} \cr & {\text{Profit of A}} = 150 \times 24 = {\text{Rs}}{\text{.}}\,{\text{3600}} \cr & {\text{Profit of B}} = 150 \times 44 = {\text{Rs}}{\text{.}}\,{\text{6600}} \cr & {\text{Profit of C}} = 150 \times 45 = {\text{Rs}}{\text{.}}\,{\text{6750}} \cr} $$

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