A, B and C are partners in a business. A, whose capital has been used for 5 months, claims $$\frac{1}{7}$$ of the profit. B whose capital has been used for 7 months, claims $$\frac{1}{5}$$ of the profit. C has invested ₹4,600 for 9 months. How much capital did A contribute?

According to the question, we find Ratio A: B:C

 A: B: C  =$$\dfrac{1}{7} :\dfrac{1}{5}: (\dfrac{1}{7}+ \dfrac {1}{5})$$

$$\Rightarrow \dfrac{1}{7}:\dfrac{1}{5}: \dfrac {35-5-7}{35}$$

$$\Rightarrow 5:7:23 $$

Let A contribute = $$x$$

so, A : C = $$x \times5 :4600\times 9 = 5 :23  $$

$$\Rightarrow x \times5 \times23 = 4600 \times9 \times5 $$

$$\Rightarrow x = \dfrac {4600 \times 9 \times 5}{5 \times 23}$$

$$\Rightarrow x = 1800 $$ Ans