A invest \(\frac{1}{4}\)th part of capital for 15 months. B gets \(\frac{2}{3}\)rd of the profit. After how many months B join the business?

05 month

Let the total investment is 4 and profit is 3.

ATQ,

                          A       :      B            Total

Investment :      1       :       3      =     4

Time            :     15      :       x                    

Profit Ratio :      15      :      3x

                           ⇑               ⇑

                           1        :     2 (given)

1R = 15

2R = 30 = 3x,

x = 10

B invest his capital for 10 months.

Therefore, B joins after (15 - 10) = 5 months