A, B and C are partners in a business. A whose money has been used for 5 months, claims \(\frac{1}{7}\) of the profit, B whose money has been used for 7 months, claims \(\frac{1}{5}\) of the profit. C had invested Rs. 4600 for 9 months. How much money did A contribute?

Rs. 1800

For \(\frac{1}{7}\) and \(\frac{1}{5}\)

Let Total profit = 35 unit

Hence,

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

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

Profit of C = 35 - (5 + 7) = 23

Now,

              A    :    B    :    C

Profit :   5    :    7    :    23

Time  :   5    :    7    :     9  

Inv.   :   1    :    1    :     \(\frac{23}{9}\)        [Inv. ratio = \(\frac{Profit.\;Ratio}{Time\;Ratio}\)]

         :   9    :    9    :    23

ATQ,

C invest = 23R = 4600

1R = 200

A's investment = 9R = 9 × 200 = Rs.1800