A, B and 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?

₹1,800

Let the total profit be 35R

Profit of A = \(\frac{1}{7}\) × 35R = 5R

Profit of B =  \(\frac{1}{5}\) × 35R = 7R

Profit of C = 35R – 5R – 7R = 23R

Let the capital of A = x & capital of B = y

As we know,

Capital × Time = Profit

 5x : 7y ∶ 4600 × 9 = 5 : 7 : 23

According to the question,

\(\frac{5x}{4600 × 9}\) =  \(\frac{5}{23}\)

 x = 9 × 200 = 1800

So, A contributes Rs. 1800