In a partnership business, B’s capital was \(\frac{1}{3}\)rd  of A’s capital. If after 7 months, B withdraw \(\frac{1}{5}\)th of his capital and after 2  more months  A withdraw \(\frac{1}{5}\)th of the capital, then their profit ratio at the end of one year will be:

171 : 55

Let investment of A = 15R

and investment of B = 5R

After withdrawal:

Investment of A = 12R

Investment of B = 4R

ATQ,  

           (A₁   :   A)    :    ( B   :   B₁)

Inv.       12   :   15   :       5   :   4

Time     3     :    9    :       7   :   5    

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Profit:  (36 + 135)   :     (35  +  20)

              171           :      55

(*Profit ratio = Inv. ratio × time ratio)