A, B and C are partners in a business. A whose money has been used for 4 months, claims \(\frac{1}{8}\) of the profit, B whose money has been used for 6 months, claims \(\frac{1}{3}\) of the profit. C had invested Rs. 1560 for 8 months. How much money did A and B contribute?

Rs. 720, Rs. 1280

For \(\frac{1}{8}\) and \(\frac{1}{3}\)

Let Total profit = 24 unit

Hence,

Profit of A = 24 × \(\frac{1}{8}\) = 3

Profit of B = 24 × \(\frac{1}{3}\) = 8

Profit of C = 24 - (3 + 8) = 13

Now,

              A    :    B    :    C

Profit :   3    :    8    :    13

Time  :   2    :    3    :     4   ⇐  (4    :    6    :    8)

Inv.   :   \(\frac{3}{2}\)    :    \(\frac{8}{3}\)    :     \(\frac{13}{4}\)        [Inv. ratio = \(\frac{Profit.\;Ratio}{Time\;Ratio}\)]

         :   18    :    32    :    39

ATQ,

C invest = 39R = 1560

1R = 40

A's investment = 18R = 18 × 40 = Rs.720

B's investment = 32R = 32 × 40 = Rs.1280