A, B and C enter into a partnership by investing their capitals in the ratio of $\frac{2}{5} : \frac{3}{4} : \frac{5}{8}$. After 4 months, A increased his capital by 50%, but B decreased his capital by 20%. What is the share of B in the total profit of ₹2,82,100 at the end of a years.

₹1,01,400

A : B : C = \(\frac{2}{5}\) : \(\frac{3}{4}\) : \(\frac{5}{8}\)

16 : 30 : 25

Let capital of A, B and C are 16x, 30x and 25x respectively.

Capital of A at the end of the year = 16x × 4 + 24x × 8 = 64x + 192x = 256x

Capital of B at the end of the year = 30x × 4 + 24x × 8 = 120x + 192x = 312x

 Capital of C at the end of the year = 25x × 12 = 300x

Capital ratio of A, B and C at the end of the year = 256x : 312x : 300x = 64x : 78x : 75x

ATQ,

64x + 78x + 75x = 282100

217x = 282100

x = \(\frac{282100}{27}\) = 1300

Profit share of B at the end of the year = 78x = 78 × 1300 = 101400